Theorems · Theorem · measure theory
MeasureTheory.ProbabilityMeasure.toWeakDualBCNN_apply
∀ {Ω : Type u_1} [inst : MeasurableSpace Ω] [inst_1 : TopologicalSpace Ω] [inst_2 : OpensMeasurableSpace Ω]
(μ : MeasureTheory.ProbabilityMeasure Ω) (f : BoundedContinuousFunction Ω NNReal),
μ.toWeakDualBCNN f = (∫⁻ (ω : Ω), ↑(f ω) ∂↑μ).toNNReal- Cited by
- 0 results in Mathlib
- Foundations
- Depth 211 from the axioms · uses propext, Classical.choice, Quot.sound
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Cites13
Mathlib declarations this one mentions in its statement or cites explicitly in its proof. Plumbing is filtered out.
- DFunLike.coestatement · cited by 62,936
- TopologicalSpacestatement and proof · cited by 24,529
- MeasurableSpacestatement and proof · cited by 13,106
- NNRealstatement and proof · cited by 4,310
- ENNReal.ofNNRealstatement · cited by 1,279
- MeasureTheory.lintegralstatement · cited by 1,152
- OpensMeasurableSpacestatement and proof · cited by 636
- BoundedContinuousFunctionstatement and proof · cited by 511
- ENNReal.toNNRealstatement · cited by 165
- MeasureTheory.ProbabilityMeasurestatement and proof · cited by 127
- WeakDualstatement · cited by 103
- MeasureTheory.ProbabilityMeasure.toMeasurestatement · cited by 78
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