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Theorems · Theorem · measure theory

MeasureTheory.Measure.isFiniteMeasure_map_iff

∀ {α : Type u_1} {β : Type u_2} {m0 : MeasurableSpace α} [mβ : MeasurableSpace β] {μ : MeasureTheory.Measure α}
  {f : α → β},
  AEMeasurable f μ → (MeasureTheory.IsFiniteMeasure (MeasureTheory.Measure.map f μ) ↔ MeasureTheory.IsFiniteMeasure μ)
Defined in
Mathlib.MeasureTheory.Measure.Typeclasses.Finite
Cited by
1 results in Mathlib
Foundations
Depth 200 from the axioms · uses propext, Classical.choice, Quot.sound
Assumes
MeasurableSpace
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Around this declaration

Dashed lines are statement dependencies; solid lines are citations in proofs.

ProbabilityTheory.HasLaw.isFiniteMeasure_iff · cited by 1HasLaw.isFiniteMeasure_iffMeasurableSpace · cited by 13106MeasurableSpaceMeasureTheory.Measure · cited by 10939MeasureTheory.MeasureMeasureTheory.IsFiniteMeasure · cited by 1078MeasureTheory.IsFiniteMea…MeasureTheory.Measure.map · cited by 858Measure.mapAEMeasurable · cited by 840AEMeasurableMeasureTheory.Measure.isFiniteMeasure_of_map · cited by 2Measure.isFiniteMeasure_o…Measure.isFiniteMeasure_map_i…CITED BYCITES

Cites6

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Cited by1

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