Theorems · Definition · measure theory

MeasureTheory.StronglyMeasurable.approx

{α : Type u_1} →
  {β : Type u_2} →
    {f : α → β} →
      [inst : TopologicalSpace β] →
        {x : MeasurableSpace α} → MeasureTheory.StronglyMeasurable f → ℕ → MeasureTheory.SimpleFunc α β

A sequence of simple functions such that ∀ x, Tendsto (fun n => hf.approx n x) atTop (𝓝 (f x)). That property is given by stronglyMeasurable.tendsto_approx.

Defined in

Mathlib.MeasureTheory.Function.StronglyMeasurable.Basic

Cited by

40 results in Mathlib

Foundations

Depth 22 from the axioms · uses propext, Classical.choice, Quot.sound

Assumes

TopologicalSpace