Theorems · Theorem · measure theory

MeasureTheory.OuterMeasure.map_iInf_comap

∀ {α : Type u_1} {ι : Sort u_2} {β : Type u_3} [Nonempty ι] {f : α → β} (m : ι → MeasureTheory.OuterMeasure β),
  (MeasureTheory.OuterMeasure.map f) (⨅ i, (MeasureTheory.OuterMeasure.comap f) (m i)) =
    ⨅ i, (MeasureTheory.OuterMeasure.map f) ((MeasureTheory.OuterMeasure.comap f) (m i))

Defined in: Mathlib.MeasureTheory.OuterMeasure.OfFunction
Cited by: 2 results in Mathlib
Foundations: Depth 167 from the axioms · uses propext, Classical.choice, Quot.sound
Assumes: Nonempty

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Cites31

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

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Cited by2

Results whose statement or proof uses this declaration.

MeasureTheory.OuterMeasure.restrict_iInfproof · cited by 1
MeasureTheory.OuterMeasure.map_biInf_comapproof · cited by 0