Theorems · Theorem · measure theory
MeasureTheory.Measure.infinitePi_map_eval
∀ {ι : Type u_1} {X : ι → Type u_2} {mX : (i : ι) → MeasurableSpace (X i)} (μ : (i : ι) → MeasureTheory.Measure (X i))
[hμ : ∀ (i : ι), MeasureTheory.IsProbabilityMeasure (μ i)] (i : ι),
MeasureTheory.Measure.map (fun x => x i) (MeasureTheory.Measure.infinitePi μ) = μ i- Defined in
- Mathlib.Probability.ProductMeasure
- Cited by
- 4 results in Mathlib
- Foundations
- Depth 283 from the axioms · uses propext, Classical.choice, Quot.sound
Around this declaration
Dashed lines are statement dependencies; solid lines are citations in proofs.
Cites7
Mathlib declarations this one mentions in its statement or cites explicitly in its proof. Plumbing is filtered out.
- MeasurableSpacestatement and proof · cited by 13,106
- MeasureTheory.Measurestatement and proof · cited by 10,939
- MeasureTheory.Measure.mapstatement · cited by 858
- MeasureTheory.IsProbabilityMeasurestatement and proof · cited by 392
- MeasureTheory.MeasurePreserving.map_eqproof · cited by 72
- MeasureTheory.Measure.infinitePistatement · cited by 48
- measurePreserving_eval_infinitePiproof · cited by 2
Cited by4
Results whose statement or proof uses this declaration.
- ProbabilityTheory.iIndepFun_infinitePiproof · cited by 3
- ProbabilityTheory.iIndepFun_uncurry_infinitePiproof · cited by 1
- MeasureTheory.Measure.infinitePi_map_eval_prodproof · cited by 0
- MeasureTheory.Measure.map_infinitePi_infinitePi_of_injproof · cited by 0