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, \mu(E)<\delta implies

 \int_E \!|f|\, \mathrm{d}\mu < \epsilon

for all  f\in \mathcal{F} .

See also

References


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