Theorems · Theorem · measure theory

ENNReal.toReal_essSup

∀ {α : Type u_1} {m : MeasurableSpace α} {μ : MeasureTheory.Measure α} {f : α → ENNReal},
  (∀ᵐ (a : α) ∂μ, f a ≠ ⊤) →
    (Filter.IsBoundedUnder (fun x1 x2 => x1 ≤ x2) (MeasureTheory.ae μ) fun i => (f i).toReal) →
      (essSup f μ).toReal = essSup (fun a => (f a).toReal) μ

Defined in

Mathlib.MeasureTheory.Function.EssSup

Cited by

1 results in Mathlib

Foundations

Depth 200 from the axioms · uses propext, Classical.choice, Quot.sound