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Theorems · Theorem · functional analysis

MeasureTheory.MemLp.aestronglyMeasurable

∀ {α : Type u_1} {ε : Type u_2} {m0 : MeasurableSpace α} [inst : ENorm ε] {μ : MeasureTheory.Measure α}
  [inst_1 : TopologicalSpace ε] {f : α → ε} {p : ENNReal},
  MeasureTheory.MemLp f p μ → MeasureTheory.AEStronglyMeasurable f μ
Defined in
Mathlib.MeasureTheory.Function.LpSeminorm.Defs
Cited by
30 results in Mathlib
Foundations
Depth 203 from the axioms · uses propext, Classical.choice, Quot.sound
Assumes
ENormTopologicalSpace

Around this declaration

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

MeasureTheory.MemLp.aemeasurable · cited by 10MemLp.aemeasurableMeasureTheory.Integrable.add_measure · cited by 6Integrable.add_measureMeasureTheory.lpNorm_add_le · cited by 5MeasureTheory.lpNorm_add_…MeasureTheory.MemLp.eLpNorm_eq_integral_rpow_norm · cited by 4MemLp.eLpNorm_eq_integral…ProbabilityTheory.IndepFun.covariance_eq_zero · cited by 4IndepFun.covariance_eq_ze…MeasureTheory.MemLp.norm · cited by 3MemLp.normMeasureTheory.MemLp.exists_boundedContinuous_eLpNorm_sub_le · cited by 3MemLp.exists_boundedConti…MeasureTheory.MemLp.exists_hasCompactSupport_eLpNorm_sub_le · cited by 3MemLp.exists_hasCompactSu…MeasureTheory.MemLp.indicator · cited by 3MemLp.indicatorMeasureTheory.MemLp.aefinStronglyMeasurable · cited by 3MemLp.aefinStronglyMeasur…MeasureTheory.eLpNorm_add_lt_top · cited by 2MeasureTheory.eLpNorm_add…MeasureTheory.ae_le_lpNorm_exponent_top · cited by 2MeasureTheory.ae_le_lpNor…MeasureTheory.MemLp.exist_eLpNorm_sub_le · cited by 2MemLp.exist_eLpNorm_sub_leMeasureTheory.unifIntegrable_of_tendsto_Lp · cited by 2MeasureTheory.unifIntegra…MeasureTheory.MemLp.induction_dense · cited by 2MemLp.induction_denseTopologicalSpace · cited by 24529TopologicalSpaceMeasurableSpace · cited by 13106MeasurableSpaceMeasureTheory.Measure · cited by 10939MeasureTheory.MeasureENNReal · cited by 9879ENNRealMeasureTheory.AEStronglyMeasurable · cited by 755MeasureTheory.AEStronglyM…MeasureTheory.MemLp · cited by 457MeasureTheory.MemLpENorm · cited by 155ENormMemLp.aestronglyMeasurableCITED BYCITES

Cites7

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Cited by30

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