Theorems · Theorem · measure theory

OrderIso.essInf_apply

∀ {α : Type u_1} {β : Type u_2} [inst : ConditionallyCompleteLattice β] {x : MeasurableSpace α} {γ : Type u_3}
  [inst_1 : ConditionallyCompleteLattice γ] (f : α → β) (μ : MeasureTheory.Measure α) (g : β ≃o γ),
  autoParam (Filter.IsBoundedUnder (fun x1 x2 => x1 ≥ x2) (MeasureTheory.ae μ) f) OrderIso.essInf_apply._auto_1 →
    autoParam (Filter.IsCoboundedUnder (fun x1 x2 => x1 ≥ x2) (MeasureTheory.ae μ) f) OrderIso.essInf_apply._auto_3 →
      autoParam (Filter.IsBoundedUnder (fun x1 x2 => x1 ≥ x2) (MeasureTheory.ae μ) fun x => g (f x))
          OrderIso.essInf_apply._auto_5 →
        autoParam (Filter.IsCoboundedUnder (fun x1 x2 => x1 ≥ x2) (MeasureTheory.ae μ) fun x => g (f x))
            OrderIso.essInf_apply._auto_7 →
          g (essInf f μ) = essInf (fun x => g (f x)) μ

Defined in

Mathlib.MeasureTheory.Function.EssSup

Cited by

0 results in Mathlib

Foundations

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

Assumes

ConditionallyCompleteLatticeConditionallyCompleteLattice