Uniform absolute continuity

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 $E$,

:

for all $fin\; mathcal\{F\}$.

ee 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