Theorems · Theorem · measure theory
MeasureTheory.Measure.dirac_apply
∀ {α : Type u_1} [inst : MeasurableSpace α] [MeasurableSingletonClass α] (a : α) (s : Set α),
(MeasureTheory.Measure.dirac a) s = s.indicator 1 a- Defined in
- Mathlib.MeasureTheory.Measure.Dirac
- Cited by
- 9 results in Mathlib
- Foundations
- Depth 173 from the axioms · uses propext, Classical.choice, Quot.sound
Around this declaration
Dashed lines are statement dependencies; solid lines are citations in proofs.
Cites19
Mathlib declarations this one mentions in its statement or cites explicitly in its proof. Plumbing is filtered out.
- DFunLike.coestatement and proof · cited by 62,936
- Setstatement and proof · cited by 53,352
- MeasurableSpacestatement and proof · cited by 13,106
- MeasureTheory.Measurestatement · cited by 10,939
- ENNRealstatement and proof · cited by 9,879
- Set.indicatorstatement and proof · cited by 723
- MeasureTheory.measure_monoproof · cited by 338
- MeasurableSingletonClassstatement and proof · cited by 230
- MeasureTheory.Measure.diracstatement and proof · cited by 210
- Set.singleton_subset_iffproof · cited by 206
- MeasurableSet.complproof · cited by 172
- Set.indicator_of_memproof · cited by 161
Cited by9
Results whose statement or proof uses this declaration.
- MeasureTheory.ae_dirac_eqproof · cited by 31
- MeasureTheory.Measure.map_diracproof · cited by 7
- MeasureTheory.restrict_diracproof · cited by 2
- MeasureTheory.Measure.tsum_indicator_apply_singletonproof · cited by 1
- MeasureTheory.dirac_withDensityproof · cited by 1
- MeasureTheory.IsZeroOneMeasure.exists_eq_diracproof · cited by 1
- ProbabilityTheory.Kernel.compProd_deterministic_applyproof · cited by 0
- MeasureTheory.diracProba_toMeasure_applyproof · cited by 0
- ProbabilityTheory.Kernel.borelMarkovFromReal_apply'proof · cited by 0