Theorems · Theorem · measure theory

essSup_le_of_ae_le

∀ {α : Type u_1} {β : Type u_2} {m : MeasurableSpace α} {μ : MeasureTheory.Measure α}
  [inst : ConditionallyCompleteLattice β] {f : α → β} (c : β),
  (f ≤ᵐ[μ] fun x => c) →
    autoParam (Filter.IsCoboundedUnder (fun x1 x2 => x1 ≤ x2) (MeasureTheory.ae μ) f) essSup_le_of_ae_le._auto_1 →
      essSup f μ ≤ c

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

ConditionallyCompleteLattice