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[[Image:Smith-Volterra set.png|thumb|right|256px|After black intervals have been removed, the white points which remain are a nowhere dense set of measure 1/2.]]
THIS SPACE OF THE WEB SITE IS INTENDED FOR SKILLED ADVISORS IN SINGAPORE. IT'S NOT MEANT TO BE USED BY MEMBERS OF MOST PEOPLE. FOR INFORMATION ON MERCHANDISE ACCESSIBLE TO MEMBERS OF THE GENERAL PUBLIC, PLEASE SEEK ADVICE FROM THE RETAIL TRADERS PART OF THIS WEBSITE. PLEASE LEARN THIS WHOLE DOCUMENT FASTIDIOUSLY EARLIER THAN YOU PROCEED. BY CLICKING "SETTLE FOR", YOU AFFIRM THAT YOU ARE A PROFESSIONAL ADVISOR AND THAT YOU CONFORM TO BE SURE BY THE TERMS AND CIRCUMSTANCES SET OUT BELOW.<br><br>How about the interest rate which fueled the Singapore Property market for the final three-four years? Presently, the 3month sibor charge is at 0.40205. This can most likely be revised up sooner than we've anticipated as a result of [http://Dietmagik.com/?qa=33944/singapore-asia-pacific-and-worldwide new condo in singapore] Federal chairman, Ms Janet Yellen indicated that the rate may rise anytime from six month later. If so, what will occur to our sibor fee? It would definitely revise up accordingly. If you're considering refinancing package right now, it could be finest if you happen to can select 1 year variable price and later refinance it again for the following 3 years fastened rate or simply merely opt for the three 12 months mounted rate of interest package deal if deemed match.<br><br>By means of its wholly-ownded subsidiary, Frasers Centrepoint Restricted ("FCL"), Fraser and Neave, Limited ("F&N") has a global portfolio of quality residential properties, serviced residences, real property and fund administration, and business properties which embody retail malls, workplaces and enterprise parks. FCL is one of Singapore's top three property companies with total belongings of over $eight billion. In Singapore, the Company presently has three tasks beneath growth - euHabitat, SBF Center and RiverTrees Residences. Far East Orchard can also be redeveloping its commercial building in Kuala Lumpur, Malaysia into a hospitality property. District 19, Freehold condominium The property managers of The Coast filed papers in the Excessive Court on July 31.<br><br>Far East, arrange by Mr Ng's father, property magnate Ng Teng Fong, last year purchased 9 sites costing about $1.6 billion in Singapore. They may yield in total 3.1 million square toes of buildable area. This is the largest land bank funding Far East has made in a single 12 months, exceeding the full of $1.54 billion invested in land and property acquisitions within the preceding six years from 2000 to 2005. In addition to the nine websites, Far East's Hong Kong-primarily based sister company Sino Land purchased the Collyer Quay website final 12 months for $one hundred sixty five.eight million. - 2007 March 14 THE ENTERPRISE OCCASIONS<br><br>You should read this earlier than continuing, as it explains the use and nondisclosure terms and situations between Templeton Asset Management Ltd ("TAML") and you (the "Agreement") which apply to the discharge of portfolio holdings info, including but not restricted to top contributors and detractors to portfolio efficiency of a number of non-U.S. domiciled collective funding schemes which can be registered as recognised schemes with the Monetary Authority of Singapore and sponsored by Franklin Templeton Investments (every a "Fund" and collectively the "Funds").<br><br>You'll be able to go for trusted property locators and I am sure they will help you to find your dream place. after i purchased lovely a peace of land plot and Martin Welch property locators group helped me find.This membership is not in existence now.But in Singapore many are available to help you Sim Lian Group has been creating houses for families in Singapore for over 35 years, first incomes an impressive monitor report in development. The Group is now recognised as an established property development, investment and building firm with an in depth portfolio of residential, business, retail and combined-use initiatives within the region. When title of property is transferred upon legal completion. Jalan Bukit Merah, Singapore 150167 Map ING Actual Property<br><br>PALM ISLES  PRIVATE CONDOMINIUM APARTMENT  FLORA DRIVE, SINGAPORE (DISTRICT 17) PARC ASTON  PERSONAL CONDOMINIUM CONDO  LEICESTER STREET, SINGAPORE (DISTRICT thirteen) PARC BLEU  PERSONAL CONDOMINIUM CONDO  JOO CHIAT PLACE, SINGAPORE (DISTRICT 15) PARC VERA  NON-PUBLIC CONDOMINIUM RESIDENCE  HOUGANG AVENUE 7, SINGAPORE (DISTRICT 19) PAYA LEBAR SQUARE  INDUSTRIAL OFFICE SPACE  PAYA LEBAR STREET, SINGAPORE (DISTRICT 14) PAYA LEBAR SQ. COMMERCIAL RETAIL SHOP SPACE  PAYA LEBAR HIGHWAY, SINGAPORE (DISTRICT 14) PRESTO @ HIGHER SERANGOON  PRIVATE CONDOMINIUM CONDOMINIUM  UPPER SERANGOON ROAD, SINGAPORE (DISTRICT 19) PROMENADE @ PELIKAT, THE  PERSONAL CONDOMINIUM CONDOMINIUM  JALAN PELIKAT, SINGAPORE (DISTRICT 19) TERRASSE  PERSONAL CONDOMINIUM CONDOMINIUM  TERRASSE LANE, SINGAPORE (DISTRICT 19)<br><br>supply of private housing to meet medium time period demand. There are 41,000 unsoldhousing units in the pipeline. The Government will inject websites that can probably yield a complete of 14,100 items in the 1H2012 Authorities Land Gross sales (GLS) Programme, much like the provision in previous GLS programmes. Of these, about 7,000 models will likely be from sites on the Confirmed Listing. These numbers take note of the ample pipeline provide and the dampening effect of the ABSD.
In [[mathematics]], the '''Smith–Volterra–Cantor set''' ('''SVC'''), '''fat Cantor set''', or '''ε-Cantor set'''<ref>Aliprantis and Burkinshaw (1981), Principles of Real Analysis</ref> is an example of a set of points on the [[real line]] '''R''' that is [[nowhere dense]] (in particular it contains no [[interval (mathematics)|interval]]s), yet has positive [[measure (mathematics)|measure]]. The Smith–Volterra–Cantor set is named after the [[mathematician]]s [[Henry John Stephen Smith|Henry Smith]], [[Vito Volterra]] and [[Georg Cantor]].
 
== Construction ==
Similar to the construction of the [[Cantor set]], the Smith–Volterra–Cantor set is constructed by removing certain intervals from the [[unit interval]] [0,&nbsp;1].
 
The process begins by removing the middle 1/4 from the interval [0,&nbsp;1] (the same as removing 1/8 on either side of the middle point at 1/2) so the remaining set is
 
:<math>\left[0, \frac{3}{8}\right] \cup \left[\frac{5}{8}, 1\right].</math>
 
The following steps consist of removing subintervals of width 1/2<sup>2''n''</sup> from the middle of each of the 2<sup>''n''&minus;1</sup> remaining intervals.  So for the second step the intervals (5/32,&nbsp;7/32) and (25/32,&nbsp;27/32) are removed, leaving
 
:<math>\left[0, \frac{5}{32}\right] \cup \left[\frac{7}{32}, \frac{3}{8}\right] \cup \left[\frac{5}{8}, \frac{25}{32}\right] \cup \left[\frac{27}{32}, 1\right].</math>
 
Continuing indefinitely with this removal, the Smith–Volterra–Cantor set is then the set of points that are never removed. The image below shows the initial set and five iterations of this process.  
 
[[Image:Smith-Volterra-Cantor set.svg|center|512px]]
 
Each subsequent iterate in the Smith–Volterra–Cantor set's construction removes proportionally less from the remaining intervals. This stands in contrast to the [[Cantor set]], where the proportion removed from each interval remains constant. Thus, the former has positive measure, while the latter zero measure.
 
== Properties ==
By construction, the Smith–Volterra–Cantor set contains no intervals and therefore has empty interior. It is also the intersection of a sequence of closed sets, which means that it is closed.
During the process, intervals of total length
 
:<math> \sum_{n=0}^{\infty} 2^n(1/2^{2n + 2}) = \frac{1}{4} + \frac{1}{8} + \frac{1}{16} + \cdots = \frac{1}{2} \,</math>
 
are removed from [0, 1], showing that the set of the remaining points has a positive measure of 1/2. This makes the Smith–Volterra–Cantor set an example of a closed set whose [[Boundary (topology)|boundary]] has positive [[Lebesgue measure]].
 
== Other fat Cantor sets ==
In general, one can remove ''r''<sub>''n''</sub> from each remaining subinterval at the ''n''-th step of the algorithm, and end up with a Cantor-like set. The resulting set will have positive measure if and only if the sum of the sequence is less than the measure of the initial interval.
 
== See also ==
* The SVC is used in the construction of [[Volterra's function]] (see external link).
* The SVC is an example of a compact set that is not Jordan measurable, see [[Jordan measure#Extension to more complicated sets]].
* The indicator function of the SVC is an example of a bounded function that is not Riemann integrable on (0,1) and moreover, is not equal almost everywhere to a Riemann integrable function, see [[Riemann integral#Examples]].
 
== References ==
 
{{Reflist}}
 
==External links==
* [http://www.macalester.edu/~bressoud/talks/AlleghenyCollege/Wrestling.pdf ''Wrestling with the Fundamental Theorem of Calculus: Volterra's function], talk by [[David Bressoud|David Marius Bressoud]]
 
{{DEFAULTSORT:Smith-Volterra-Cantor set}}
[[Category:Sets of real numbers]]
[[Category:Measure theory]]
[[Category:Topological spaces]]
[[Category:Fractals]]

Latest revision as of 11:45, 17 December 2014

THIS SPACE OF THE WEB SITE IS INTENDED FOR SKILLED ADVISORS IN SINGAPORE. IT'S NOT MEANT TO BE USED BY MEMBERS OF MOST PEOPLE. FOR INFORMATION ON MERCHANDISE ACCESSIBLE TO MEMBERS OF THE GENERAL PUBLIC, PLEASE SEEK ADVICE FROM THE RETAIL TRADERS PART OF THIS WEBSITE. PLEASE LEARN THIS WHOLE DOCUMENT FASTIDIOUSLY EARLIER THAN YOU PROCEED. BY CLICKING "SETTLE FOR", YOU AFFIRM THAT YOU ARE A PROFESSIONAL ADVISOR AND THAT YOU CONFORM TO BE SURE BY THE TERMS AND CIRCUMSTANCES SET OUT BELOW.

How about the interest rate which fueled the Singapore Property market for the final three-four years? Presently, the 3month sibor charge is at 0.40205. This can most likely be revised up sooner than we've anticipated as a result of new condo in singapore Federal chairman, Ms Janet Yellen indicated that the rate may rise anytime from six month later. If so, what will occur to our sibor fee? It would definitely revise up accordingly. If you're considering refinancing package right now, it could be finest if you happen to can select 1 year variable price and later refinance it again for the following 3 years fastened rate or simply merely opt for the three 12 months mounted rate of interest package deal if deemed match.

By means of its wholly-ownded subsidiary, Frasers Centrepoint Restricted ("FCL"), Fraser and Neave, Limited ("F&N") has a global portfolio of quality residential properties, serviced residences, real property and fund administration, and business properties which embody retail malls, workplaces and enterprise parks. FCL is one of Singapore's top three property companies with total belongings of over $eight billion. In Singapore, the Company presently has three tasks beneath growth - euHabitat, SBF Center and RiverTrees Residences. Far East Orchard can also be redeveloping its commercial building in Kuala Lumpur, Malaysia into a hospitality property. District 19, Freehold condominium The property managers of The Coast filed papers in the Excessive Court on July 31.

Far East, arrange by Mr Ng's father, property magnate Ng Teng Fong, last year purchased 9 sites costing about $1.6 billion in Singapore. They may yield in total 3.1 million square toes of buildable area. This is the largest land bank funding Far East has made in a single 12 months, exceeding the full of $1.54 billion invested in land and property acquisitions within the preceding six years from 2000 to 2005. In addition to the nine websites, Far East's Hong Kong-primarily based sister company Sino Land purchased the Collyer Quay website final 12 months for $one hundred sixty five.eight million. - 2007 March 14 THE ENTERPRISE OCCASIONS

You should read this earlier than continuing, as it explains the use and nondisclosure terms and situations between Templeton Asset Management Ltd ("TAML") and you (the "Agreement") which apply to the discharge of portfolio holdings info, including but not restricted to top contributors and detractors to portfolio efficiency of a number of non-U.S. domiciled collective funding schemes which can be registered as recognised schemes with the Monetary Authority of Singapore and sponsored by Franklin Templeton Investments (every a "Fund" and collectively the "Funds").

You'll be able to go for trusted property locators and I am sure they will help you to find your dream place. after i purchased lovely a peace of land plot and Martin Welch property locators group helped me find.This membership is not in existence now.But in Singapore many are available to help you Sim Lian Group has been creating houses for families in Singapore for over 35 years, first incomes an impressive monitor report in development. The Group is now recognised as an established property development, investment and building firm with an in depth portfolio of residential, business, retail and combined-use initiatives within the region. When title of property is transferred upon legal completion. Jalan Bukit Merah, Singapore 150167 Map ING Actual Property

PALM ISLES PRIVATE CONDOMINIUM APARTMENT FLORA DRIVE, SINGAPORE (DISTRICT 17) PARC ASTON PERSONAL CONDOMINIUM CONDO LEICESTER STREET, SINGAPORE (DISTRICT thirteen) PARC BLEU PERSONAL CONDOMINIUM CONDO JOO CHIAT PLACE, SINGAPORE (DISTRICT 15) PARC VERA NON-PUBLIC CONDOMINIUM RESIDENCE HOUGANG AVENUE 7, SINGAPORE (DISTRICT 19) PAYA LEBAR SQUARE INDUSTRIAL OFFICE SPACE PAYA LEBAR STREET, SINGAPORE (DISTRICT 14) PAYA LEBAR SQ. COMMERCIAL RETAIL SHOP SPACE PAYA LEBAR HIGHWAY, SINGAPORE (DISTRICT 14) PRESTO @ HIGHER SERANGOON PRIVATE CONDOMINIUM CONDOMINIUM UPPER SERANGOON ROAD, SINGAPORE (DISTRICT 19) PROMENADE @ PELIKAT, THE PERSONAL CONDOMINIUM CONDOMINIUM JALAN PELIKAT, SINGAPORE (DISTRICT 19) TERRASSE PERSONAL CONDOMINIUM CONDOMINIUM TERRASSE LANE, SINGAPORE (DISTRICT 19)

supply of private housing to meet medium time period demand. There are 41,000 unsoldhousing units in the pipeline. The Government will inject websites that can probably yield a complete of 14,100 items in the 1H2012 Authorities Land Gross sales (GLS) Programme, much like the provision in previous GLS programmes. Of these, about 7,000 models will likely be from sites on the Confirmed Listing. These numbers take note of the ample pipeline provide and the dampening effect of the ABSD.

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