Theorems · Theorem · measure theory

essSup_mono_measure

∀ {α : Type u_1} {β : Type u_2} {m : MeasurableSpace α} {μ ν : MeasureTheory.Measure α}
  [inst : ConditionallyCompleteLattice β] {f : α → β},
  ν.AbsolutelyContinuous μ →
    autoParam (Filter.IsCoboundedUnder (fun x1 x2 => x1 ≤ x2) (MeasureTheory.ae ν) f) essSup_mono_measure._auto_1 →
      autoParam (Filter.IsBoundedUnder (fun x1 x2 => x1 ≤ x2) (MeasureTheory.ae μ) f) essSup_mono_measure._auto_3 →
        essSup f ν ≤ essSup f μ

Defined in

Mathlib.MeasureTheory.Function.EssSup

Cited by

2 results in Mathlib

Foundations

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

Assumes

ConditionallyCompleteLattice