Theorems · Theorem · measure theory
MeasureTheory.ProbabilityMeasure.measureReal_eq_coe_coeFn
∀ {Ω : Type u_1} [inst : MeasurableSpace Ω] (ν : MeasureTheory.ProbabilityMeasure Ω) (s : Set Ω), (↑ν).real s = ↑(ν s)- Cited by
- 4 results in Mathlib
- Foundations
- Depth 177 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.
Cites10
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
- Realstatement · cited by 25,697
- MeasurableSpacestatement and proof · cited by 13,106
- NNRealstatement · cited by 4,310
- NNReal.toRealstatement and proof · cited by 1,260
- MeasureTheory.Measure.realstatement · cited by 530
- ENNReal.toNNRealproof · cited by 165
- MeasureTheory.ProbabilityMeasurestatement and proof · cited by 127
- MeasureTheory.ProbabilityMeasure.toMeasurestatement and proof · cited by 78
Cited by4
Results whose statement or proof uses this declaration.
- MeasureTheory.tendsto_iff_forall_lipschitz_integral_tendstoproof · cited by 1
- MeasureTheory.tendsto_of_forall_isClosed_limsup_real_le'proof · cited by 1
- IsPiSystem.tendsto_probabilityMeasure_biUnionproof · cited by 1
- MeasureTheory.ProbabilityMeasure.toNNReal_measureReal_eq_coeFnproof · cited by 0