Theorems · Theorem · measure theory
MeasureTheory.Measure.isProbabilityMeasure_map
∀ {α : Type u_1} {β : Type u_2} {m0 : MeasurableSpace α} [inst : MeasurableSpace β] {μ : MeasureTheory.Measure α}
[MeasureTheory.IsProbabilityMeasure μ] {f : α → β},
AEMeasurable f μ → MeasureTheory.IsProbabilityMeasure (MeasureTheory.Measure.map f μ)- Cited by
- 19 results in Mathlib
- Foundations
- Depth 199 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
- AEMeasurablestatement and proof · cited by 840
- MeasureTheory.IsProbabilityMeasurestatement and proof · cited by 392
- MeasureTheory.IsProbabilityMeasure.measure_univproof · cited by 135
- MeasureTheory.Measure.map_apply_of_aemeasurableproof · cited by 36
Cited by21
Results whose statement or proof uses this declaration.
- MeasureTheory.TendstoInDistribution.tendstostatement · cited by 5
- ProbabilityTheory.iIndepFun_iff_map_fun_eq_infinitePi_map₀proof · cited by 4
- MeasureTheory.TendstoInDistribution.continuous_compproof · cited by 3
- ProbabilityTheory.iIndepFun.map_fun_eq_infinitePi_map₀proof · cited by 3
- MeasureTheory.Measure.infinitePi_map_piproof · cited by 2
- MeasureTheory.tendstoInDistribution_of_tendstoInMeasure_subproof · cited by 2
- ProbabilityTheory.iIndepFun_uncurryproof · cited by 2
- ProbabilityTheory.HasGaussianLaw.of_subsingletonproof · cited by 1
- MeasureTheory.Measure.isProbabilityMeasure_map_iffproof · cited by 1
- MeasureTheory.measureReal_abs_inner_gt_le_integral_charFunproof · cited by 1
- MeasureTheory.taylorWithinEval_charFun_two_zeroproof · cited by 1
- MeasureTheory.tendstoInDistribution_of_identDistribproof · cited by 1