Theorems · Theorem · measure theory

MeasureTheory.all_ae_ofReal_f_le_bound

Deprecated since 2026-01-26Use MeasureTheory.ae_norm_ofReal_f_le_bound instead.

∀ {α : Type u_1} {β : Type u_2} {m : MeasurableSpace α} {μ : MeasureTheory.Measure α} [inst : NormedAddCommGroup β]
  {F : ℕ → α → β} {f : α → β} {bound : α → ℝ},
  (∀ (n : ℕ), ∀ᵐ (a : α) ∂μ, ‖F n a‖ ≤ bound a) →
    (∀ᵐ (a : α) ∂μ, Filter.Tendsto (fun n => F n a) Filter.atTop (nhds (f a))) →
      ∀ᵐ (a : α) ∂μ, ENNReal.ofReal ‖f a‖ ≤ ENNReal.ofReal (bound a)

Alias of MeasureTheory.ae_norm_ofReal_f_le_bound.

Defined in

Mathlib.MeasureTheory.Function.L1Space.HasFiniteIntegral

Cited by

0 results in Mathlib

Foundations

Depth 174 from the axioms · uses propext, Classical.choice, Quot.sound

Assumes

NormedAddCommGroup