Theorems · Theorem · measure theory
MeasureTheory.laverage_eq_lintegral
∀ {α : Type u_1} {m0 : MeasurableSpace α} (μ : MeasureTheory.Measure α) [MeasureTheory.IsProbabilityMeasure μ]
(f : α → ENNReal), ⨍⁻ (x : α), f x ∂μ = ∫⁻ (x : α), f x ∂μ- Defined in
- Mathlib.MeasureTheory.Integral.Average
- Cited by
- 6 results in Mathlib
- Foundations
- Depth 177 from the axioms · uses propext, Classical.choice, Quot.sound
Around this declaration
Dashed lines are statement dependencies; solid lines are citations in proofs.
Cites9
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
- MeasureTheory.Measurestatement and proof · cited by 10,939
- ENNRealstatement and proof · cited by 9,879
- one_smulproof · cited by 1,374
- MeasureTheory.lintegralstatement and proof · cited by 1,152
- MeasureTheory.IsProbabilityMeasurestatement and proof · cited by 392
- inv_oneproof · cited by 301
- MeasureTheory.IsProbabilityMeasure.measure_univproof · cited by 135
- MeasureTheory.laveragestatement · cited by 44
Cited by6
Results whose statement or proof uses this declaration.
- MeasureTheory.exists_lintegral_leproof · cited by 1
- MeasureTheory.measure_le_lintegral_posproof · cited by 0
- MeasureTheory.exists_notMem_null_le_lintegralproof · cited by 0
- MeasureTheory.exists_notMem_null_lintegral_leproof · cited by 0
- MeasureTheory.exists_le_lintegralproof · cited by 0
- MeasureTheory.measure_lintegral_le_posproof · cited by 0