Theorems · Theorem · measure theory
MeasureTheory.FiniteMeasure.toWeakDualBCNN_apply
∀ {Ω : Type u_1} [inst : MeasurableSpace Ω] [inst_1 : TopologicalSpace Ω] [inst_2 : OpensMeasurableSpace Ω]
(μ : MeasureTheory.FiniteMeasure Ω) (f : BoundedContinuousFunction Ω NNReal),
μ.toWeakDualBCNN f = (∫⁻ (x : Ω), ↑(f x) ∂↑μ).toNNReal- Cited by
- 1 results in Mathlib
- Foundations
- Depth 210 from the axioms · uses propext, Classical.choice, Quot.sound
Around this declaration
Dashed lines are statement dependencies; solid lines are citations in proofs.
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.FiniteMeasurestatement and proof · cited by 150
- WeakDualstatement · cited by 103
- MeasureTheory.FiniteMeasure.toMeasurestatement · cited by 87
Cited by1
Results whose statement or proof uses this declaration.
- MeasureTheory.FiniteMeasure.tendsto_iff_forall_lintegral_tendstoproof · cited by 5