Theorems · Theorem · measure theory

ae_lt_of_essSup_lt

∀ {α : Type u_1} {β : Type u_2} {m : MeasurableSpace α} {μ : MeasureTheory.Measure α}
  [inst : ConditionallyCompleteLinearOrder β] {x : β} {f : α → β},
  essSup f μ < x →
    autoParam (Filter.IsBoundedUnder (fun x1 x2 => x1 ≤ x2) (MeasureTheory.ae μ) f) ae_lt_of_essSup_lt._auto_1 →
      ∀ᵐ (y : α) ∂μ, f y < x

Defined in

Mathlib.MeasureTheory.Function.EssSup

Cited by

4 results in Mathlib

Foundations

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

Assumes

ConditionallyCompleteLinearOrder