Jump to navigation Jump to search

General

Display information for equation id:math.11436.10 on revision:11436

* Page found: Γ-convergence (eq math.11436.10)

(force rerendering)

Occurrences on the following pages:

Hash: 2d417401580207d19f4160c2da6e63ad

TeX (original user input): 

F(x)\le\liminf_{n\to\infty} F_n(x_n).

TeX (checked): 

F(x)\leq \liminf _{n\to \infty }F_{n}(x_{n}).

LaTeXML (experimental; uses MathML) rendering

MathML (4.781 KB / 927 B) :

F ⁢ ( x ) ≤ lim inf n → ∞ ⁡ F n ⁢ ( x n ) . 𝐹 𝑥 subscript limit-infimum → 𝑛 subscript 𝐹 𝑛 subscript 𝑥 𝑛 {\displaystyle F(x)\leq\liminf_{{n\to\infty}}F_{n}(x_{n}).} 
<math xmlns="http://www.w3.org/1998/Math/MathML" id="p1.1.m1.1" class="ltx_Math" alttext="{\displaystyle F(x)\leq\liminf_{{n\to\infty}}F_{n}(x_{n}).}" display="inline">
  <semantics id="p1.1.m1.1a">
    <mrow id="p1.1.m1.1.15" xref="p1.1.m1.1.15.2.cmml">
      <mrow id="p1.1.m1.1.15.2" xref="p1.1.m1.1.15.2.cmml">
        <mrow id="p1.1.m1.1.15.2.1" xref="p1.1.m1.1.15.2.1.cmml">
          <mi id="p1.1.m1.1.1" xref="p1.1.m1.1.1.cmml">F</mi>
          <mo id="p1.1.m1.1.15.2.1.1" xref="p1.1.m1.1.15.2.1.1.cmml">⁢</mo>
          <mrow id="p1.1.m1.1.15.2.1.2" xref="p1.1.m1.1.15.2.1.cmml">
            <mo stretchy="false" id="p1.1.m1.1.2" xref="p1.1.m1.1.15.2.1.cmml">(</mo>
            <mi id="p1.1.m1.1.3" xref="p1.1.m1.1.3.cmml">x</mi>
            <mo stretchy="false" id="p1.1.m1.1.4" xref="p1.1.m1.1.15.2.1.cmml">)</mo>
          </mrow>
        </mrow>
        <mo id="p1.1.m1.1.5" xref="p1.1.m1.1.5.cmml">≤</mo>
        <mrow id="p1.1.m1.1.15.2.2" xref="p1.1.m1.1.15.2.2.cmml">
          <munder id="p1.1.m1.1.15.2.2.1" xref="p1.1.m1.1.15.2.2.1.cmml">
            <mo movablelimits="false" id="p1.1.m1.1.6" xref="p1.1.m1.1.6.cmml">lim inf</mo>
            <mrow id="p1.1.m1.1.7.1" xref="p1.1.m1.1.7.1.cmml">
              <mi id="p1.1.m1.1.7.1.1" xref="p1.1.m1.1.7.1.1.cmml">n</mi>
              <mo id="p1.1.m1.1.7.1.2" xref="p1.1.m1.1.7.1.2.cmml">→</mo>
              <mi mathvariant="normal" id="p1.1.m1.1.7.1.3" xref="p1.1.m1.1.7.1.3.cmml">∞</mi>
            </mrow>
          </munder>
          <mo id="p1.1.m1.1.15.2.2a" xref="p1.1.m1.1.15.2.2.cmml">⁡</mo>
          <mrow id="p1.1.m1.1.15.2.2.2" xref="p1.1.m1.1.15.2.2.2.cmml">
            <msub id="p1.1.m1.1.15.2.2.2.2" xref="p1.1.m1.1.15.2.2.2.2.cmml">
              <mi id="p1.1.m1.1.8" xref="p1.1.m1.1.8.cmml">F</mi>
              <mi id="p1.1.m1.1.9.1" xref="p1.1.m1.1.9.1.cmml">n</mi>
            </msub>
            <mo id="p1.1.m1.1.15.2.2.2.1" xref="p1.1.m1.1.15.2.2.2.1.cmml">⁢</mo>
            <mrow id="p1.1.m1.1.15.2.2.2.3" xref="p1.1.m1.1.15.2.2.2.3.2.cmml">
              <mo stretchy="false" id="p1.1.m1.1.10" xref="p1.1.m1.1.15.2.2.2.3.2.cmml">(</mo>
              <msub id="p1.1.m1.1.15.2.2.2.3.2" xref="p1.1.m1.1.15.2.2.2.3.2.cmml">
                <mi id="p1.1.m1.1.11" xref="p1.1.m1.1.11.cmml">x</mi>
                <mi id="p1.1.m1.1.12.1" xref="p1.1.m1.1.12.1.cmml">n</mi>
              </msub>
              <mo stretchy="false" id="p1.1.m1.1.13" xref="p1.1.m1.1.15.2.2.2.3.2.cmml">)</mo>
            </mrow>
          </mrow>
        </mrow>
      </mrow>
      <mo id="p1.1.m1.1.14" xref="p1.1.m1.1.15.2.cmml">.</mo>
    </mrow>
    <annotation-xml encoding="MathML-Content" id="p1.1.m1.1b">
      <apply id="p1.1.m1.1.15.2.cmml" xref="p1.1.m1.1.15">
        <leq id="p1.1.m1.1.5.cmml" xref="p1.1.m1.1.5"/>
        <apply id="p1.1.m1.1.15.2.1.cmml" xref="p1.1.m1.1.15.2.1">
          <times id="p1.1.m1.1.15.2.1.1.cmml" xref="p1.1.m1.1.15.2.1.1"/>
          <ci id="p1.1.m1.1.1.cmml" xref="p1.1.m1.1.1">𝐹</ci>
          <ci id="p1.1.m1.1.3.cmml" xref="p1.1.m1.1.3">𝑥</ci>
        </apply>
        <apply id="p1.1.m1.1.15.2.2.cmml" xref="p1.1.m1.1.15.2.2">
          <apply id="p1.1.m1.1.15.2.2.1.cmml" xref="p1.1.m1.1.15.2.2.1">
            <csymbol cd="ambiguous" id="p1.1.m1.1.15.2.2.1.1.cmml" xref="p1.1.m1.1.15.2.2.1">subscript</csymbol>
            <csymbol cd="latexml" id="p1.1.m1.1.6.cmml" xref="p1.1.m1.1.6">limit-infimum</csymbol>
            <apply id="p1.1.m1.1.7.1.cmml" xref="p1.1.m1.1.7.1">
              <ci id="p1.1.m1.1.7.1.2.cmml" xref="p1.1.m1.1.7.1.2">→</ci>
              <ci id="p1.1.m1.1.7.1.1.cmml" xref="p1.1.m1.1.7.1.1">𝑛</ci>
              <infinity id="p1.1.m1.1.7.1.3.cmml" xref="p1.1.m1.1.7.1.3"/>
            </apply>
          </apply>
          <apply id="p1.1.m1.1.15.2.2.2.cmml" xref="p1.1.m1.1.15.2.2.2">
            <times id="p1.1.m1.1.15.2.2.2.1.cmml" xref="p1.1.m1.1.15.2.2.2.1"/>
            <apply id="p1.1.m1.1.15.2.2.2.2.cmml" xref="p1.1.m1.1.15.2.2.2.2">
              <csymbol cd="ambiguous" id="p1.1.m1.1.15.2.2.2.2.1.cmml" xref="p1.1.m1.1.15.2.2.2.2">subscript</csymbol>
              <ci id="p1.1.m1.1.8.cmml" xref="p1.1.m1.1.8">𝐹</ci>
              <ci id="p1.1.m1.1.9.1.cmml" xref="p1.1.m1.1.9.1">𝑛</ci>
            </apply>
            <apply id="p1.1.m1.1.15.2.2.2.3.2.cmml" xref="p1.1.m1.1.15.2.2.2.3">
              <csymbol cd="ambiguous" id="p1.1.m1.1.15.2.2.2.3.2.1.cmml" xref="p1.1.m1.1.15.2.2.2.3">subscript</csymbol>
              <ci id="p1.1.m1.1.11.cmml" xref="p1.1.m1.1.11">𝑥</ci>
              <ci id="p1.1.m1.1.12.1.cmml" xref="p1.1.m1.1.12.1">𝑛</ci>
            </apply>
          </apply>
        </apply>
      </apply>
    </annotation-xml>
    <annotation encoding="application/x-tex" id="p1.1.m1.1c">{\displaystyle F(x)\leq\liminf_{{n\to\infty}}F_{n}(x_{n}).}</annotation>
  </semantics>
</math>

SVG (10.755 KB / 3.872 KB) :

upper F left parenthesis x right parenthesis less than or equals limit inf Underscript n right arrow normal infinity Endscripts upper F Subscript n Baseline left parenthesis x Subscript n Baseline right parenthesis period

SVG (MathML can be enabled via browser plugin) rendering

MathML (1.194 KB / 452 B) :

F ( x ) ≤ lim inf n → ∞ F n ( x n ) . {\displaystyle F(x)\leq \liminf _{n\to \infty }F_{n}(x_{n}).} 
<math xmlns="http://www.w3.org/1998/Math/MathML" display="block" alttext="{\displaystyle F(x)\leq \liminf _{n\to \infty }F_{n}(x_{n}).}">
  <semantics>
    <mrow class="MJX-TeXAtom-ORD">
      <mstyle displaystyle="true" scriptlevel="0">
        <mi>F</mi>
        <mo stretchy="false">(</mo>
        <mi>x</mi>
        <mo stretchy="false">)</mo>
        <mo>&#x2264;<!-- ≤ --></mo>
        <munder>
          <mo movablelimits="true" form="prefix">lim&#x2006;inf</mo>
          <mrow class="MJX-TeXAtom-ORD">
            <mi>n</mi>
            <mo stretchy="false">&#x2192;<!-- → --></mo>
            <mi mathvariant="normal">&#x221E;<!-- ∞ --></mi>
          </mrow>
        </munder>
        <msub>
          <mi>F</mi>
          <mrow class="MJX-TeXAtom-ORD">
            <mi>n</mi>
          </mrow>
        </msub>
        <mo stretchy="false">(</mo>
        <msub>
          <mi>x</mi>
          <mrow class="MJX-TeXAtom-ORD">
            <mi>n</mi>
          </mrow>
        </msub>
        <mo stretchy="false">)</mo>
        <mo>.</mo>
      </mstyle>
    </mrow>
    <annotation encoding="application/x-tex">{\displaystyle F(x)\leq \liminf _{n\to \infty }F_{n}(x_{n}).}</annotation>
  </semantics>
</math>

SVG (8.858 KB / 3.583 KB) :

{\displaystyle F(x)\leq \liminf _{n\to \infty }F_{n}(x_{n}).}

Translations to Computer Algebra Systems

Translation to Maple

In Maple:

Translation to Mathematica

In Mathematica:

Similar pages

Calculated based on the variables occurring on the entire Γ-convergence page

Identifiers

MathML observations

0results

0results

no statistics present please run the maintenance script ExtractFeatures.php

0 results

0 results

Retrieved from "https://en.formulasearchengine.com/wiki/Special:FormulaInfo"