Theorems · Definition · measure theory

MeasureTheory.AEStronglyMeasurable

{α : Type u_1} →
  {β : Type u_2} →
    [TopologicalSpace β] →
      [m : MeasurableSpace α] →
        {m₀ : MeasurableSpace α} →
          (α → β) → autoParam (MeasureTheory.Measure α) MeasureTheory.AEStronglyMeasurable._auto_1 → Prop

A function is AEStronglyMeasurable with respect to a measure μ if it is almost everywhere equal to the limit of a sequence of simple functions. One can specify the sigma-algebra according to which simple functions are taken using the AEStronglyMeasurable[m] notation in the MeasureTheory scope.

Defined in

Mathlib.MeasureTheory.Function.StronglyMeasurable.AEStronglyMeasurable

Cited by

755 results in Mathlib

Foundations

Depth 171 from the axioms, rests on 4,665 definitions · uses propext, Classical.choice, Quot.sound

Assumes

TopologicalSpaceMeasurableSpace