Theorems · Theorem · measure theory
MeasureTheory.lintegral_dirac
∀ {α : Type u_1} [inst : MeasurableSpace α] [MeasurableSingletonClass α] (a : α) (f : α → ENNReal),
∫⁻ (a : α), f a ∂MeasureTheory.Measure.dirac a = f a- Cited by
- 13 results in Mathlib
- Foundations
- Depth 196 from the axioms · uses propext, Classical.choice, Quot.sound
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.
- MeasurableSpacestatement and proof · cited by 13,106
- ENNRealstatement and proof · cited by 9,879
- mul_oneproof · cited by 3,885
- MeasureTheory.lintegralstatement · cited by 1,152
- MeasurableSingletonClassstatement and proof · cited by 230
- MeasureTheory.Measure.diracstatement · cited by 210
- MeasureTheory.IsProbabilityMeasure.measure_univproof · cited by 135
- MeasureTheory.lintegral_constproof · cited by 123
- MeasureTheory.lintegral_congr_aeproof · cited by 95
- MeasureTheory.ae_eq_diracproof · cited by 5
Cited by13
Results whose statement or proof uses this declaration.
- MeasureTheory.lintegral_countable'proof · cited by 4
- MeasureTheory.lintegral_countproof · cited by 3
- MeasureTheory.integrable_diracproof · cited by 3
- MeasureTheory.lintegral_singletonproof · cited by 2
- MeasureTheory.setLIntegral_diracproof · cited by 2
- MeasureTheory.integral_of_ae_eq_zero_or_oneproof · cited by 2
- ProbabilityTheory.ofReal_cdfproof · cited by 2
- MeasureTheory.Measure.dirac_compProd_applyproof · cited by 1
- MeasureTheory.eLpNorm_diracproof · cited by 1
- ProbabilityTheory.posterior_boolKernel_apply_falseproof · cited by 0
- ProbabilityTheory.posterior_boolKernel_apply_trueproof · cited by 0
- ProbabilityTheory.Kernel.lintegral_deterministicproof · cited by 0