Theorems · Theorem · measure theory
MeasureTheory.Measure.dirac_apply_of_mem
∀ {α : Type u_1} [inst : MeasurableSpace α] {s : Set α} {a : α}, a ∈ s → (MeasureTheory.Measure.dirac a) s = 1- Defined in
- Mathlib.MeasureTheory.Measure.Dirac
- Cited by
- 7 results in Mathlib
- Foundations
- Depth 172 from the axioms · uses propext, Classical.choice, Quot.sound
- Assumes
- MeasurableSpace
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.
- 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.univproof · cited by 3,945
- le_antisymmproof · cited by 2,068
- Set.indicatorproof · cited by 723
- MeasureTheory.measure_monoproof · cited by 338
- Set.subset_univproof · cited by 228
- MeasureTheory.Measure.diracstatement and proof · cited by 210
- MeasurableSet.univproof · cited by 178
Cited by7
Results whose statement or proof uses this declaration.
- MeasureTheory.Measure.dirac_applyproof · cited by 9
- MeasureTheory.Measure.pi_of_emptyproof · cited by 6
- MeasureTheory.Measure.count_eq_zero_iffproof · cited by 3
- MeasureTheory.IsZeroOneMeasure.exists_eq_diracproof · cited by 1
- MeasureTheory.diracProba_toMeasure_apply_of_memproof · cited by 0
- MeasureTheory.Measure.dirac_ne_zeroproof · cited by 0
- torusIntegral_dim0proof · cited by 0