Theorems · Theorem · measure theory

MeasureTheory.OuterMeasure.comap_ofFunction

∀ {α : Type u_1} {m : Set α → ENNReal} {m_empty : m ∅ = 0} {β : Type u_2} (f : β → α),
  Monotone m ∨ Function.Surjective f →
    (MeasureTheory.OuterMeasure.comap f) (MeasureTheory.OuterMeasure.ofFunction m m_empty) =
      MeasureTheory.OuterMeasure.ofFunction (fun s => m (f '' s)) ⋯

Defined in: Mathlib.MeasureTheory.OuterMeasure.OfFunction
Cited by: 2 results in Mathlib
Foundations: Depth 163 from the axioms · uses propext, Classical.choice, Quot.sound

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Cites27

Mathlib declarations this one mentions in its statement or cites explicitly in its proof. Plumbing is filtered out.

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Monotonestatement and proof · cited by 1,397

Cited by2

Results whose statement or proof uses this declaration.

MeasureTheory.OuterMeasure.comap_boundedByproof · cited by 1
MeasureTheory.OuterMeasure.restrict_ofFunctionproof · cited by 0