Theorems · Theorem · probability
MeasureTheory.Measure.deterministic_comp_eq_map
∀ {α : Type u_1} {β : Type u_2} {mα : MeasurableSpace α} {mβ : MeasurableSpace β} {μ : MeasureTheory.Measure α}
{f : α → β} (hf : Measurable f), μ.bind ⇑(ProbabilityTheory.Kernel.deterministic f hf) = MeasureTheory.Measure.map f μ- Cited by
- 11 results in Mathlib
- Foundations
- Depth 214 from the axioms · uses propext, Classical.choice, Quot.sound
Around this declaration
Dashed lines are statement dependencies; solid lines are citations in proofs.
Cites9
Mathlib declarations this one mentions in its statement or cites explicitly in its proof. Plumbing is filtered out.
- DFunLike.coestatement · cited by 62,936
- MeasurableSpacestatement and proof · cited by 13,106
- MeasureTheory.Measurestatement and proof · cited by 10,939
- Measurablestatement and proof · cited by 1,499
- ProbabilityTheory.Kernelstatement · cited by 1,281
- MeasureTheory.Measure.mapstatement · cited by 858
- MeasureTheory.Measure.bindstatement · cited by 173
- ProbabilityTheory.Kernel.deterministicstatement · cited by 57
- MeasureTheory.Measure.bind_dirac_eq_mapproof · cited by 1
Cited by11
Results whose statement or proof uses this declaration.
- MeasureTheory.Measure.compProd_mapproof · cited by 4
- MeasureTheory.Measure.swap_compproof · cited by 4
- MeasureTheory.Measure.id_compproof · cited by 4
- MeasureTheory.Measure.compProd_id_eq_copy_compproof · cited by 2
- MeasureTheory.Measure.prodMkLeft_comp_compProdproof · cited by 1
- MeasureTheory.Measure.compProd_deterministicproof · cited by 1
- MeasureTheory.Measure.copy_comp_mapproof · cited by 0
- ProbabilityTheory.deterministic_comp_posteriorproof · cited by 0
- MeasureTheory.Measure.prod_comp_leftproof · cited by 0
- ProbabilityTheory.Kernel.HasSubgaussianMGF.id_map_iffproof · cited by 0
- ProbabilityTheory.condIndepFun_iff_condDistrib_prod_ae_eq_prodMkRightproof · cited by 0