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Theorems · Theorem · measure theory

MeasureTheory.MemLp.sub

∀ {α : Type u_1} {E : Type u_2} {m : MeasurableSpace α} [inst : NormedAddCommGroup E] {p : ENNReal}
  {μ : MeasureTheory.Measure α} {f g : α → E},
  MeasureTheory.MemLp f p μ → MeasureTheory.MemLp g p μ → MeasureTheory.MemLp (f - g) p μ
Defined in
Mathlib.MeasureTheory.Function.LpSeminorm.TriangleInequality
Cited by
17 results in Mathlib
Foundations
Depth 220 from the axioms · uses propext, Classical.choice, Quot.sound
Assumes
NormedAddCommGroup

Around this declaration

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

MeasureTheory.lpNorm_add_le · cited by 5MeasureTheory.lpNorm_add_…ProbabilityTheory.covariance_add_left · cited by 4ProbabilityTheory.covaria…ProbabilityTheory.evariance_lt_top · cited by 3ProbabilityTheory.evarian…MeasureTheory.unifIntegrable_of_tendsto_Lp · cited by 2MeasureTheory.unifIntegra…ProbabilityTheory.variance_add_const · cited by 2ProbabilityTheory.varianc…ProbabilityTheory.covarianceBilinDual_apply · cited by 2ProbabilityTheory.covaria…ProbabilityTheory.HasIndepIncrements.isPreBrownianReal_of_hasLaw · cited by 1HasIndepIncrements.isPreB…MeasureTheory.MemLp.exists_boundedContinuous_integral_rpow_sub_le · cited by 1MemLp.exists_boundedConti…MeasureTheory.MemLp.exists_hasCompactSupport_integral_rpow_sub_le · cited by 1MemLp.exists_hasCompactSu…ProbabilityTheory.IndepFun.hasGaussianLaw_sub_of_sub · cited by 1IndepFun.hasGaussianLaw_s…ProbabilityTheory.covariance_sub_sub · cited by 1ProbabilityTheory.covaria…MeasureTheory.Lp.tendsto_Lp_iff_tendsto_eLpNorm'' · cited by 0Lp.tendsto_Lp_iff_tendsto…MeasureTheory.Lp.dense_hasCompactSupport_contDiff · cited by 0Lp.dense_hasCompactSuppor…MeasureTheory.indicatorConstLp_sub · cited by 0MeasureTheory.indicatorCo…MeasureTheory.lpNorm_sub_le_lpNorm_sub_add_lpNorm_sub · cited by 0MeasureTheory.lpNorm_sub_…NormedAddCommGroup · cited by 15752NormedAddCommGroupMeasurableSpace · cited by 13106MeasurableSpaceMeasureTheory.Measure · cited by 10939MeasureTheory.MeasureENNReal · cited by 9879ENNRealsub_eq_add_neg · cited by 1023sub_eq_add_negMeasureTheory.MemLp · cited by 457MeasureTheory.MemLpMeasureTheory.MemLp.add · cited by 24MemLp.addMeasureTheory.MemLp.neg · cited by 12MemLp.negMemLp.subCITED BYCITES

Cites8

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Cited by17

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