Theorems · Theorem · measure theory
MeasureTheory.withDensity_zero
∀ {α : Type u_1} {m0 : MeasurableSpace α} {μ : MeasureTheory.Measure α}, μ.withDensity 0 = 0- Cited by
- 4 results in Mathlib
- Foundations
- Depth 204 from the axioms · uses propext, Classical.choice, Quot.sound
Around this declaration
Dashed lines are statement dependencies; solid lines are citations in proofs.
Cites13
Mathlib declarations this one mentions in its statement or cites explicitly in its proof. Plumbing is filtered out.
- DFunLike.coeproof · cited by 62,936
- Setproof · cited by 53,352
- MeasurableSpacestatement and proof · cited by 13,106
- MeasureTheory.Measurestatement and proof · cited by 10,939
- ENNRealstatement and proof · cited by 9,879
- MeasurableSetproof · cited by 3,075
- MulZeroClass.zero_mulproof · cited by 1,625
- MeasureTheory.Measure.extproof · cited by 308
- MeasureTheory.Measure.withDensitystatement · cited by 265
- Set.univ_interproof · cited by 258
- MeasureTheory.Measure.restrict_applyproof · cited by 159
- MeasureTheory.lintegral_constproof · cited by 123
Cited by4
Results whose statement or proof uses this declaration.
- MeasureTheory.Measure.withDensity_rnDeriv_leproof · cited by 9
- ProbabilityTheory.Kernel.withDensity_zeroproof · cited by 1
- MeasureTheory.Measure.MutuallySingular.haveLebesgueDecompositionproof · cited by 1
- ProbabilityTheory.rnDeriv_gaussianRealproof · cited by 0