Theorems · Theorem · measure theory
MeasureTheory.condExp_congr_ae
∀ {α : Type u_1} {E : Type u_3} {m m₀ : MeasurableSpace α} {μ : MeasureTheory.Measure α} {f g : α → E}
[inst : NormedAddCommGroup E] [inst_1 : NormedSpace ℝ E] [CompleteSpace E], f =ᵐ[μ] g → μ[f | m] =ᵐ[μ] μ[g | m]- Cited by
- 17 results in Mathlib
- Foundations
- Depth 297 from the axioms · uses propext, Classical.choice, Quot.sound
Around this declaration
Dashed lines are statement dependencies; solid lines are citations in proofs.
Cites22
Mathlib declarations this one mentions in its statement or cites explicitly in its proof. Plumbing is filtered out.
- Realstatement and proof · cited by 25,697
- NormedAddCommGroupstatement and proof · cited by 15,752
- MeasurableSpacestatement and proof · cited by 13,106
- NormedSpacestatement and proof · cited by 12,499
- MeasureTheory.Measurestatement and proof · cited by 10,939
- CompleteSpacestatement and proof · cited by 2,532
- MeasureTheory.aestatement and proof · cited by 2,352
- Filter.EventuallyEqstatement and proof · cited by 1,912
- MeasureTheory.AEEqFunproof · cited by 856
- MeasureTheory.Lpproof · cited by 715
- MeasureTheory.SigmaFiniteproof · cited by 526
- Filter.EventuallyEq.symmproof · cited by 408
Cited by17
Results whose statement or proof uses this declaration.
- MeasureTheory.condExp_bilin_of_aestronglyMeasurable_leftproof · cited by 5
- MeasureTheory.condExp_of_aestronglyMeasurable'proof · cited by 2
- MeasureTheory.martingale_natproof · cited by 2
- MeasureTheory.condExp_bilin_of_stronglyMeasurable_leftproof · cited by 2
- ProbabilityTheory.condVar_congr_aeproof · cited by 1
- ProbabilityTheory.condVar_of_ae_eq_zero_or_oneproof · cited by 1
- MeasureTheory.condExp_aestronglyMeasurable_bilin_of_boundproof · cited by 1
- MeasureTheory.condLExp_ofRealproof · cited by 1
- MeasureTheory.condExp_congr_ae_trimproof · cited by 1
- MeasureTheory.condExp_indicator_auxproof · cited by 1
- MeasureTheory.Integrable.uniformIntegrable_condExpproof · cited by 1