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Theorems · Theorem · measure theory

MeasureTheory.integrable_condExp

∀ {α : Type u_1} {E : Type u_3} {m m₀ : MeasurableSpace α} {μ : MeasureTheory.Measure α} {f : α → E}
  [inst : NormedAddCommGroup E] [inst_1 : NormedSpace ℝ E] [CompleteSpace E], MeasureTheory.Integrable μ[f | m] μ
Defined in
Mathlib.MeasureTheory.Function.ConditionalExpectation.Basic
Cited by
28 results in Mathlib
Foundations
Depth 297 from the axioms · uses propext, Classical.choice, Quot.sound
Assumes
NormedAddCommGroupNormedSpaceCompleteSpace

Around this declaration

Dashed lines are statement dependencies; solid lines are citations in proofs.

MeasureTheory.ae_eq_condExp_of_forall_setIntegral_eq · cited by 12MeasureTheory.ae_eq_condE…MeasureTheory.Martingale.integrable · cited by 10Martingale.integrableMeasureTheory.condExp_restrict_ae_eq_restrict · cited by 8MeasureTheory.condExp_res…MeasureTheory.condExp_ae_eq_restrict_of_measurableSpace_eq_on · cited by 6MeasureTheory.condExp_ae_…MeasureTheory.condExp_condExp_of_le · cited by 6MeasureTheory.condExp_con…MeasureTheory.condExp_stronglyMeasurable_bilin_of_bound · cited by 3MeasureTheory.condExp_str…MeasureTheory.MemLp.condExp · cited by 3MemLp.condExpMeasureTheory.martingale_martingalePart · cited by 2MeasureTheory.martingale_…MeasureTheory.integral_abs_condExp_le · cited by 2MeasureTheory.integral_ab…MeasureTheory.submartingale_nat · cited by 2MeasureTheory.submartinga…MeasureTheory.submartingale_of_setIntegral_le · cited by 2MeasureTheory.submartinga…ContinuousLinearMap.comp_condExp_comm · cited by 2ContinuousLinearMap.comp_…InformationTheory.klDiv_map_le · cited by 2InformationTheory.klDiv_m…MeasureTheory.condExp_ae_eq_restrict_zero · cited by 2MeasureTheory.condExp_ae_…MeasureTheory.integral_norm_condExp_rpow_le · cited by 2MeasureTheory.integral_no…Real · cited by 25697RealNormedAddCommGroup · cited by 15752NormedAddCommGroupMeasurableSpace · cited by 13106MeasurableSpaceNormedSpace · cited by 12499NormedSpaceMeasureTheory.Measure · cited by 10939MeasureTheory.MeasureCompleteSpace · cited by 2532CompleteSpaceMeasureTheory.Integrable · cited by 1367MeasureTheory.IntegrableMeasureTheory.SigmaFinite · cited by 526MeasureTheory.SigmaFiniteFilter.EventuallyEq.symm · cited by 408EventuallyEq.symmMeasureTheory.Measure.trim · cited by 286Measure.trimMeasureTheory.condExp · cited by 234MeasureTheory.condExpMeasureTheory.condExp_of_not_sigmaFinite · cited by 28MeasureTheory.condExp_of_…MeasureTheory.Integrable.congr · cited by 28Integrable.congrMeasureTheory.condExp_of_not_le · cited by 27MeasureTheory.condExp_of_…MeasureTheory.integrable_zero · cited by 22MeasureTheory.integrable_…MeasureTheory.integrable_cond…CITED BYCITES

Cites17

Mathlib declarations this one mentions in its statement or cites explicitly in its proof. Plumbing is filtered out.

Cited by28

Results whose statement or proof uses this declaration.