Theorems · Theorem · measure theory

MeasureTheory.tendstoInMeasure_of_ne_top

∀ {α : Type u_1} {ι : Type u_2} {E : Type u_4} {m : MeasurableSpace α} {μ : MeasureTheory.Measure α} [inst : EDist E]
  {f : ι → α → E} {l : Filter ι} {g : α → E},
  (∀ (ε : ENNReal), 0 < ε → ε ≠ ⊤ → Filter.Tendsto (fun i => μ {x | ε ≤ edist (f i x) (g x)}) l (nhds 0)) →
    MeasureTheory.TendstoInMeasure μ f l g

Defined in

Mathlib.MeasureTheory.Function.ConvergenceInMeasure

Cited by

4 results in Mathlib

Foundations

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

Assumes

EDist