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Theorems · Theorem · measure theory

MeasureTheory.OuterMeasure.smul_dirac_apply

∀ {α : Type u_1} (a : ENNReal) (b : α) (s : Set α),
  (a • MeasureTheory.OuterMeasure.dirac b) s = s.indicator (fun x => a) b
Defined in
Mathlib.MeasureTheory.OuterMeasure.Operations
Cited by
1 results in Mathlib
Foundations
Depth 142 from the axioms · uses propext, Classical.choice, Quot.sound
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Around this declaration

Dashed lines are statement dependencies; solid lines are citations in proofs.

PMF.toOuterMeasure_apply · cited by 16PMF.toOuterMeasure_applyDFunLike.coe · cited by 62936DFunLike.coeSet · cited by 53352SetENNReal · cited by 9879ENNRealmul_one · cited by 3885mul_oneSet.indicator · cited by 723Set.indicatorMeasureTheory.OuterMeasure · cited by 287MeasureTheory.OuterMeasuresmul_apply · cited by 229smul_applySet.indicator_mul_right · cited by 7Set.indicator_mul_rightMeasureTheory.OuterMeasure.dirac · cited by 7OuterMeasure.diracOuterMeasure.smul_dirac_applyCITED BYCITES

Cites9

Mathlib declarations this one mentions in its statement or cites explicitly in its proof. Plumbing is filtered out.

Cited by1

Results whose statement or proof uses this declaration.