Theorems · Theorem · measure theory
MeasureTheory.measurePreserving_fst
∀ {α : Type u_1} {β : Type u_2} [inst : MeasurableSpace α] [inst_1 : MeasurableSpace β] {μ : MeasureTheory.Measure α}
{ν : MeasureTheory.Measure β} [MeasureTheory.SFinite ν] [MeasureTheory.IsProbabilityMeasure ν],
MeasureTheory.MeasurePreserving Prod.fst (μ.prod ν) μ- Defined in
- Mathlib.MeasureTheory.Measure.Prod
- Cited by
- 4 results in Mathlib
- Foundations
- Depth 219 from the axioms · uses propext, Classical.choice, Quot.sound
Around this declaration
Dashed lines are statement dependencies; solid lines are citations in proofs.
Cites11
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
- one_smulproof · cited by 1,374
- MeasureTheory.SFinitestatement and proof · cited by 449
- MeasureTheory.IsProbabilityMeasurestatement and proof · cited by 392
- MeasureTheory.Measure.prodstatement · cited by 353
- MeasureTheory.MeasurePreservingstatement · cited by 259
- MeasureTheory.IsProbabilityMeasure.measure_univproof · cited by 135
- measurable_fstproof · cited by 79
- MeasureTheory.Measure.map_fst_prodproof · cited by 9
Cited by4
Results whose statement or proof uses this declaration.
- ProbabilityTheory.indepFun_prod₀proof · cited by 2
- ProbabilityTheory.variance_add_prodproof · cited by 1
- ProbabilityTheory.charFun_map_add_prod_eq_mulproof · cited by 0
- ProbabilityTheory.charFunDual_map_add_prod_eq_mulproof · cited by 0