Theorems · Theorem · measure theory
MeasureTheory.withDensity_add_measure
∀ {α : Type u_1} {m : MeasurableSpace α} (μ ν : MeasureTheory.Measure α) (f : α → ENNReal),
(μ + ν).withDensity f = μ.withDensity f + ν.withDensity f- Cited by
- 2 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.
Cites12
Mathlib declarations this one mentions in its statement or cites explicitly in its proof. Plumbing is filtered out.
- 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
- MeasureTheory.Measure.restrictproof · cited by 1,646
- MeasureTheory.lintegralproof · cited by 1,152
- MeasureTheory.Measure.extproof · cited by 308
- MeasureTheory.Measure.withDensitystatement · cited by 265
- MeasureTheory.withDensity_applyproof · cited by 73
- MeasureTheory.lintegral_add_measureproof · cited by 13
- MeasureTheory.Measure.restrict_addproof · cited by 9
Cited by2
Results whose statement or proof uses this declaration.
- MeasureTheory.Measure.rnDeriv_withDensity_withDensity_rnDeriv_leftproof · cited by 1
- ProbabilityTheory.Kernel.withDensity_add_leftproof · cited by 0