Methods of contour integration

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

$ϵ>0$

there exists

$\delta >0$

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

$\underset{E}{\int }\left|f\right|d\mu <ϵ$

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

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