Theorems · Theorem · measure theory
MeasureTheory.Measure.bind_zero_left
∀ {α : Type u_1} {β : Type u_2} {mα : MeasurableSpace α} {mβ : MeasurableSpace β} (f : α → MeasureTheory.Measure β),
MeasureTheory.Measure.bind 0 f = 0- Defined in
- Mathlib.MeasureTheory.Measure.GiryMonad
- Cited by
- 5 results in Mathlib
- Foundations
- Depth 211 from the axioms · uses propext, Classical.choice, Quot.sound
Around this declaration
Dashed lines are statement dependencies; solid lines are citations in proofs.
Cites6
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.bindstatement · cited by 173
- MeasureTheory.Measure.joinproof · cited by 26
- MeasureTheory.Measure.map_zeroproof · cited by 17
- MeasureTheory.Measure.join_zeroproof · cited by 1
Cited by5
Results whose statement or proof uses this declaration.
- ProbabilityTheory.Kernel.comp_zeroproof · cited by 8
- MeasureTheory.Measure.zero_prodproof · cited by 4
- MeasureTheory.Measure.parallelComp_comp_compProdproof · cited by 1
- MeasureTheory.Measure.comp_compProd_commproof · cited by 1
- ProbabilityTheory.Kernel.HasSubgaussianMGF.zero_measureproof · cited by 0