Theorems · Theorem · measure theory
MeasureTheory.measurePreserving_eval
∀ {ι : Type u_1} {α : ι → Type u_3} [inst : Fintype ι] [inst_1 : (i : ι) → MeasurableSpace (α i)]
(μ : (i : ι) → MeasureTheory.Measure (α i)) [∀ (i : ι), MeasureTheory.IsProbabilityMeasure (μ i)] (i : ι),
MeasureTheory.MeasurePreserving (Function.eval i) (MeasureTheory.Measure.pi μ) (μ i)- Defined in
- Mathlib.MeasureTheory.Constructions.Pi
- Cited by
- 5 results in Mathlib
- Foundations
- Depth 232 from the axioms · uses propext, Classical.choice, Quot.sound
Around this declaration
Dashed lines are statement dependencies; solid lines are citations in proofs.
Cites15
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
- ENNRealproof · cited by 9,879
- Fintypestatement and proof · cited by 7,736
- Finset.univproof · cited by 3,473
- one_smulproof · cited by 1,374
- Finset.eraseproof · cited by 455
- MeasureTheory.IsProbabilityMeasurestatement and proof · cited by 392
- MeasureTheory.MeasurePreservingstatement · cited by 259
- Function.evalstatement · cited by 140
- MeasureTheory.IsProbabilityMeasure.measure_univproof · cited by 135
- MeasureTheory.Measure.pistatement · cited by 130
Cited by5
Results whose statement or proof uses this declaration.
- measurePreserving_eval_infinitePiproof · cited by 2
- ProbabilityTheory.iIndepFun_piproof · cited by 2
- MeasureTheory.integral_comp_evalproof · cited by 1
- ProbabilityTheory.charFunDual_map_sum_pi_eq_prodproof · cited by 1
- ProbabilityTheory.variance_sum_piproof · cited by 1