Theorems · Theorem · probability
ProbabilityTheory.Kernel.lintegral_id
∀ {α : Type u_1} {mα : MeasurableSpace α} [MeasurableSingletonClass α] {f : α → ENNReal} (a : α),
∫⁻ (a : α), f a ∂ProbabilityTheory.Kernel.id a = f a- Defined in
- Mathlib.Probability.Kernel.Basic
- Cited by
- 0 results in Mathlib
- Foundations
- Depth 197 from the axioms · uses propext, Classical.choice, Quot.sound
- Assumes
- MeasurableSingletonClass
Around this declaration
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Cites10
Mathlib declarations this one mentions in its statement or cites explicitly in its proof. Plumbing is filtered out.
- DFunLike.coestatement · cited by 62,936
- MeasurableSpacestatement and proof · cited by 13,106
- MeasureTheory.Measurestatement and proof · cited by 10,939
- ENNRealstatement and proof · cited by 9,879
- ProbabilityTheory.Kernelstatement · cited by 1,281
- MeasureTheory.lintegralstatement and proof · cited by 1,152
- MeasurableSingletonClassstatement and proof · cited by 230
- ProbabilityTheory.Kernel.idstatement · cited by 72
- ProbabilityTheory.Kernel.id_applyproof · cited by 15
- MeasureTheory.lintegral_diracproof · cited by 13
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