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Theorems · Theorem · functional analysis

MeasureTheory.memLp_const

∀ {α : Type u_1} {E : Type u_4} {m0 : MeasurableSpace α} {p : ENNReal} {μ : MeasureTheory.Measure α}
  [inst : NormedAddCommGroup E] (c : E) [MeasureTheory.IsFiniteMeasure μ], MeasureTheory.MemLp (fun x => c) p μ
Defined in
Mathlib.MeasureTheory.Function.LpSeminorm.Basic
Cited by
16 results in Mathlib
Foundations
Depth 208 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.

MeasureTheory.MemLp.of_bound · cited by 6MemLp.of_boundProbabilityTheory.covariance_add_left · cited by 4ProbabilityTheory.covaria…ProbabilityTheory.evariance_lt_top · cited by 3ProbabilityTheory.evarian…MeasureTheory.MemLp.toLp_const · cited by 3MemLp.toLp_constProbabilityTheory.evariance_eq_top · cited by 2ProbabilityTheory.evarian…MeasureTheory.memLp_indicator_const · cited by 2MeasureTheory.memLp_indic…ProbabilityTheory.variance_add_const · cited by 2ProbabilityTheory.varianc…ProbabilityTheory.covarianceBilinDual_apply · cited by 2ProbabilityTheory.covaria…MeasureTheory.indicatorConstLp_univ · cited by 1MeasureTheory.indicatorCo…MeasureTheory.memLp_of_bounded · cited by 1MeasureTheory.memLp_of_bo…ProbabilityTheory.variance_le_expectation_sq · cited by 1ProbabilityTheory.varianc…ProbabilityTheory.covarianceBilin_map_const_add · cited by 1ProbabilityTheory.covaria…ProbabilityTheory.strong_law_Lp · cited by 0ProbabilityTheory.strong_…MeasureTheory.Lp.norm_const · cited by 0Lp.norm_constMeasureTheory.Lp.norm_const' · cited by 0Lp.norm_const'NormedAddCommGroup · cited by 15752NormedAddCommGroupMeasurableSpace · cited by 13106MeasurableSpaceMeasureTheory.Measure · cited by 10939MeasureTheory.MeasureENNReal · cited by 9879ENNRealMeasureTheory.IsFiniteMeasure · cited by 1078MeasureTheory.IsFiniteMea…MeasureTheory.MemLp · cited by 457MeasureTheory.MemLpenorm_ne_top · cited by 82enorm_ne_topMeasureTheory.memLp_const_enorm · cited by 3MeasureTheory.memLp_const…MeasureTheory.memLp_constCITED BYCITES

Cites8

Mathlib declarations this one mentions in its statement or cites explicitly in its proof. Plumbing is filtered out.

Cited by16

Results whose statement or proof uses this declaration.