Theorems · Theorem · measure theory

MeasureTheory.ae_tendsto_enorm

∀ {α : Type u_1} {m : MeasurableSpace α} {μ : MeasureTheory.Measure α} {ε : Type u_7} [inst : TopologicalSpace ε]
  [inst_1 : ESeminormedAddMonoid ε] {F' : ℕ → α → ε} {f' : α → ε},
  (∀ᵐ (a : α) ∂μ, Filter.Tendsto (fun n => F' n a) Filter.atTop (nhds (f' a))) →
    ∀ᵐ (a : α) ∂μ, Filter.Tendsto (fun n => ‖F' n a‖ₑ) Filter.atTop (nhds ‖f' a‖ₑ)

Defined in

Mathlib.MeasureTheory.Function.L1Space.HasFiniteIntegral

Cited by

2 results in Mathlib

Foundations

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

Assumes

TopologicalSpaceESeminormedAddMonoid