Uniform absolute continuity

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

ε > 0

there exists

δ > 0

such that for any measurable set E, μ(E) < δ implies

∫ | f | dμ < ε
E

for all f\in \mathcal{F} .

[edit] See also

[edit] 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