Methods of contour integration

In mathematical analysis, a collection ${\mathcal {F}}$ of real-valued and integrable functions is uniformly absolutely continuous, if for every

$\epsilon >0$

there exists

$\delta >0$

such that for any measurable set $E$, $\mu (E)<\delta$ implies

$\int _{E}|f|d\mu <\epsilon$

for all $f\in {\mathcal {F}}$.

See also

• Absolute continuity
• Uniform integrability

References

• J. J. Benedetto (1976). Real Variable and Integration - section 3.3, p. 89. B. G. Teubner, Stuttgart. ISBN 3-519-02209-5
• C. W. Burrill (1972). Measure, Integration, and Probability - section 9-5, p. 180. McGraw-Hill. ISBN 0-07-009223-0

Template:Mathanalysis-stub