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Theorems · Theorem · measure theory

MeasureTheory.AEStronglyMeasurable.sub

∀ {α : Type u_1} {β : Type u_2} [inst : TopologicalSpace β] {m m₀ : MeasurableSpace α} {μ : MeasureTheory.Measure α}
  {f g : α → β} [inst_1 : AddGroup β] [IsTopologicalAddGroup β],
  MeasureTheory.AEStronglyMeasurable f μ →
    MeasureTheory.AEStronglyMeasurable g μ → MeasureTheory.AEStronglyMeasurable (f - g) μ
Defined in
Mathlib.MeasureTheory.Function.StronglyMeasurable.AEStronglyMeasurable
Cited by
21 results in Mathlib
Foundations
Depth 174 from the axioms · uses propext, Classical.choice, Quot.sound
Assumes
TopologicalSpaceAddGroupIsTopologicalAddGroup

Around this declaration

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

ProbabilityTheory.covariance_map · cited by 5ProbabilityTheory.covaria…MeasureTheory.MemLp.exists_boundedContinuous_eLpNorm_sub_le · cited by 3MemLp.exists_boundedConti…MeasureTheory.MemLp.exists_hasCompactSupport_eLpNorm_sub_le · cited by 3MemLp.exists_hasCompactSu…MeasureTheory.tendsto_setToFun_of_L1 · cited by 3MeasureTheory.tendsto_set…MeasureTheory.AEStronglyMeasurable.fun_sub · cited by 3AEStronglyMeasurable.fun_…MeasureTheory.Lp.ae_eq_of_forall_setIntegral_eq' · cited by 2Lp.ae_eq_of_forall_setInt…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_denseMeasureTheory.tendsto_lintegral_norm_of_dominated_convergence · cited by 2MeasureTheory.tendsto_lin…MeasureTheory.Lp.memLp_of_cauchy_tendsto · cited by 1Lp.memLp_of_cauchy_tendstoMeasureTheory.Lp.cauchy_tendsto_of_tendsto · cited by 1Lp.cauchy_tendsto_of_tend…MeasureTheory.integral_tendsto_of_tendsto_of_monotone · cited by 1MeasureTheory.integral_te…MeasureTheory.tendsto_integral_norm_approxOn_sub · cited by 1MeasureTheory.tendsto_int…LipschitzWith.integral_inv_smul_sub_mul_tendsto_integral_lineDeriv_mul · cited by 1LipschitzWith.integral_in…TopologicalSpace · cited by 24529TopologicalSpaceMeasurableSpace · cited by 13106MeasurableSpaceMeasureTheory.Measure · cited by 10939MeasureTheory.MeasureAddGroup · cited by 4410AddGroupIsTopologicalAddGroup · cited by 1394IsTopologicalAddGroupMeasureTheory.AEStronglyMeasurable · cited by 755MeasureTheory.AEStronglyM…MeasureTheory.AEStronglyMeasurable.mk · cited by 82AEStronglyMeasurable.mkMeasureTheory.AEStronglyMeasurable.ae_eq_mk · cited by 77AEStronglyMeasurable.ae_e…MeasureTheory.AEStronglyMeasurable.stronglyMeasurable_mk · cited by 71AEStronglyMeasurable.stro…Filter.EventuallyEq.sub · cited by 19EventuallyEq.subMeasureTheory.StronglyMeasurable.sub · cited by 18StronglyMeasurable.subAEStronglyMeasurable.subCITED BYCITES

Cites11

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Cited by21

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