Theorems · Theorem · measure theory

MeasureTheory.tendstoInMeasure_iff_enorm

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

TendstoInMeasure expressed with an extended norm instead of a distance.

Defined in

Mathlib.MeasureTheory.Function.ConvergenceInMeasure

Cited by

1 results in Mathlib

Foundations

Depth 172 from the axioms · uses propext, Classical.choice, Quot.sound

Assumes

SeminormedAddCommGroup