Theorems · Theorem · measure theory
measurePreserving_eval_infinitePi
∀ {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.MeasurePreserving (Function.eval i) (MeasureTheory.Measure.infinitePi μ) (μ i)- Defined in
- Mathlib.Probability.ProductMeasure
- Cited by
- 2 results in Mathlib
- Foundations
- Depth 282 from the axioms · uses propext, Classical.choice, Quot.sound
Around this declaration
Dashed lines are statement dependencies; solid lines are citations in proofs.
Cites18
Mathlib declarations this one mentions in its statement or cites explicitly in its proof. Plumbing is filtered out.
- DFunLike.coeproof · cited by 62,936
- Setproof · cited by 53,352
- MeasurableSpacestatement and proof · cited by 13,106
- MeasureTheory.Measurestatement and proof · cited by 10,939
- MeasurableSetproof · cited by 3,075
- MeasureTheory.Measure.mapproof · cited by 858
- MeasureTheory.IsProbabilityMeasurestatement and proof · cited by 392
- MeasureTheory.Measure.extproof · cited by 308
- MeasureTheory.MeasurePreservingstatement · cited by 259
- Function.evalstatement and proof · cited by 140
- measurable_pi_applyproof · cited by 77
- MeasureTheory.MeasurePreserving.map_eqproof · cited by 72
Cited by2
Results whose statement or proof uses this declaration.
- MeasureTheory.Measure.infinitePi_map_evalproof · cited by 4
- ProbabilityTheory.exists_hasLaw_indepFunproof · cited by 1