Theorems · Theorem · measure theory
MeasureTheory.dirac_withDensity
∀ {α : Type u_1} {m0 : MeasurableSpace α} [MeasurableSingletonClass α] (f : α → ENNReal) (a : α),
(MeasureTheory.Measure.dirac a).withDensity f = f a • MeasureTheory.Measure.dirac a- Cited by
- 1 results in Mathlib
- Foundations
- Depth 204 from the axioms · uses propext, Classical.choice, Quot.sound
- Assumes
- MeasurableSingletonClass
Around this declaration
Dashed lines are statement dependencies; solid lines are citations in proofs.
Cites15
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
- mul_oneproof · cited by 3,885
- MeasurableSetproof · cited by 3,075
- MulZeroClass.mul_zeroproof · cited by 2,091
- MeasureTheory.Measure.extproof · cited by 308
- MeasureTheory.Measure.withDensitystatement · cited by 265
- MeasurableSingletonClassstatement and proof · cited by 230
- MeasureTheory.Measure.diracstatement and proof · cited by 210
- mul_iteproof · cited by 159
Cited by1
Results whose statement or proof uses this declaration.
- MeasureTheory.count_withDensityproof · cited by 0