Theorems · Theorem · measure theory

MeasureTheory.StronglyMeasurable.tendsto_approxBounded_ae

∀ {α : Type u_1} {β : Type u_5} {f : α → β} [inst : NormedAddCommGroup β] [inst_1 : NormedSpace ℝ β]
  {m m0 : MeasurableSpace α} {μ : MeasureTheory.Measure α} (hf : MeasureTheory.StronglyMeasurable f) {c : ℝ},
  (∀ᵐ (x : α) ∂μ, ‖f x‖ ≤ c) →
    ∀ᵐ (x : α) ∂μ, Filter.Tendsto (fun n => (hf.approxBounded c n) x) Filter.atTop (nhds (f x))

Defined in

Mathlib.MeasureTheory.Function.StronglyMeasurable.Basic

Cited by

1 results in Mathlib

Foundations

Depth 171 from the axioms · uses propext, Classical.choice, Quot.sound

Assumes

NormedAddCommGroupNormedSpace