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Theorems · Theorem · measure theory

MeasureTheory.integrable_const

∀ {α : Type u_1} {β : Type u_2} {m : MeasurableSpace α} {μ : MeasureTheory.Measure α} [inst : NormedAddCommGroup β]
  [MeasureTheory.IsFiniteMeasure μ] (c : β), MeasureTheory.Integrable (fun x => c) μ
Defined in
Mathlib.MeasureTheory.Function.L1Space.Integrable
Cited by
73 results in Mathlib
Foundations
Depth 202 from the axioms · uses propext, Classical.choice, Quot.sound
Assumes
NormedAddCommGroupMeasureTheory.IsFiniteMeasure

Around this declaration

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

ProbabilityTheory.integral_id_multivariateGaussian · cited by 5ProbabilityTheory.integra…MeasureTheory.condExp_const · cited by 5MeasureTheory.condExp_con…InformationTheory.integrable_klFun_rnDeriv_iff · cited by 5InformationTheory.integra…indicator_indepFun_pi_of_prod_bcf · cited by 4indicator_indepFun_pi_of_…ProbabilityTheory.IsGaussian.memLp_id · cited by 4IsGaussian.memLp_idInformationTheory.toReal_klDiv_smul_right_eq_smul_left · cited by 3InformationTheory.toReal_…ProbabilityTheory.covariance_add_const_left · cited by 3ProbabilityTheory.covaria…isCompact_setOfPred_finiteMeasure_mass_le_compl_isCompact_le · cited by 2isCompact_setOfPred_finit…MeasureTheory.charFun_conv · cited by 2MeasureTheory.charFun_convMeasureTheory.integral_sub_average · cited by 2MeasureTheory.integral_su…ProbabilityTheory.variance_add_const · cited by 2ProbabilityTheory.varianc…ProbabilityTheory.condDistrib_ae_eq_condExp · cited by 2ProbabilityTheory.condDis…ae_eq_const_or_exists_average_ne_compl · cited by 2ae_eq_const_or_exists_ave…MeasureTheory.tendsto_setToFun_filter_of_norm_le_const · cited by 2MeasureTheory.tendsto_set…MeasureTheory.condExp_le_nonneg_const · cited by 2MeasureTheory.condExp_le_…NormedAddCommGroup · cited by 15752NormedAddCommGroupMeasurableSpace · cited by 13106MeasurableSpaceMeasureTheory.Measure · cited by 10939MeasureTheory.MeasureMeasureTheory.Integrable · cited by 1367MeasureTheory.IntegrableMeasureTheory.IsFiniteMeasure · cited by 1078MeasureTheory.IsFiniteMea…MeasureTheory.integrable_const_iff · cited by 2MeasureTheory.integrable_…MeasureTheory.integrable_constCITED BYCITES

Cites6

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Cited by73

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