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Theorems · Theorem · measure theory

MeasureTheory.AEStronglyMeasurable.norm

∀ {α : Type u_1} {m₀ : MeasurableSpace α} {μ : MeasureTheory.Measure α} {β : Type u_5} [inst : SeminormedAddCommGroup β]
  {f : α → β}, MeasureTheory.AEStronglyMeasurable f μ → MeasureTheory.AEStronglyMeasurable (fun x => ‖f x‖) μ
Defined in
Mathlib.MeasureTheory.Function.StronglyMeasurable.AEStronglyMeasurable
Cited by
30 results in Mathlib
Foundations
Depth 175 from the axioms · uses propext, Classical.choice, Quot.sound
Assumes
SeminormedAddCommGroup

Around this declaration

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

MeasureTheory.Integrable.norm · cited by 63Integrable.normMeasureTheory.norm_integral_le_integral_norm · cited by 25MeasureTheory.norm_integr…MeasureTheory.integrable_norm_iff · cited by 19MeasureTheory.integrable_…ProbabilityTheory.integrable_comp_iff · cited by 6ProbabilityTheory.integra…MeasureTheory.Integrable.convolution_integrand · cited by 6Integrable.convolution_in…MeasureTheory.AECover.integrable_of_integral_norm_bounded · cited by 6AECover.integrable_of_int…MeasureTheory.integrable_prod_iff · cited by 5MeasureTheory.integrable_…MeasureTheory.MemLp.eLpNorm_eq_integral_rpow_norm · cited by 4MemLp.eLpNorm_eq_integral…ProbabilityTheory.IsGaussian.memLp_id · cited by 4IsGaussian.memLp_idMeasureTheory.MemLp.norm · cited by 3MemLp.normProbabilityTheory.integrable_compProd_iff · cited by 3ProbabilityTheory.integra…MeasureTheory.integral_norm_eq_lintegral_enorm · cited by 3MeasureTheory.integral_no…MeasureTheory.L1.norm_eq_integral_norm · cited by 3L1.norm_eq_integral_normMeasureTheory.MemLp.condExp · cited by 3MemLp.condExpMeasureTheory.MemLp.norm_rpow_div · cited by 2MemLp.norm_rpow_divReal · cited by 25697RealMeasurableSpace · cited by 13106MeasurableSpaceMeasureTheory.Measure · cited by 10939MeasureTheory.MeasureNorm.norm · cited by 5413Norm.normSeminormedAddCommGroup · cited by 2671SeminormedAddCommGroupMeasureTheory.AEStronglyMeasurable · cited by 755MeasureTheory.AEStronglyM…Continuous.comp_aestronglyMeasurable · cited by 77Continuous.comp_aestrongl…continuous_norm · cited by 36continuous_normAEStronglyMeasurable.normCITED BYCITES

Cites8

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Cited by30

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