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Theorems · Theorem · functional analysis

MeasureTheory.MemLp.coeFn_toLp

∀ {α : Type u_1} {E : Type u_4} {m : MeasurableSpace α} {p : ENNReal} {μ : MeasureTheory.Measure α}
  [inst : NormedAddCommGroup E] {f : α → E} (hf : MeasureTheory.MemLp f p μ), ↑↑(MeasureTheory.MemLp.toLp f hf) =ᵐ[μ] f
Defined in
Mathlib.MeasureTheory.Function.LpSpace.Basic
Cited by
35 results in Mathlib
Foundations
Depth 222 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.indicatorConstLp_coeFn · cited by 15MeasureTheory.indicatorCo…MeasureTheory.Lp.norm_toLp · cited by 7Lp.norm_toLpMeasureTheory.lpMeasSubgroupToLpTrim_ae_eq · cited by 6MeasureTheory.lpMeasSubgr…SchwartzMap.coeFn_toLp · cited by 5SchwartzMap.coeFn_toLpProbabilityTheory.uncenteredCovarianceBilinDual_apply · cited by 4ProbabilityTheory.uncente…MeasureTheory.Lp.edist_toLp_toLp · cited by 4Lp.edist_toLp_toLpintegral_withDensity_eq_integral_smul · cited by 4integral_withDensity_eq_i…ContinuousLinearMap.comp_memLp' · cited by 3ContinuousLinearMap.comp_…MeasureTheory.integral_condExpL2_eq · cited by 3MeasureTheory.integral_co…MeasureTheory.Lp.coeFn_lpSMul · cited by 2Lp.coeFn_lpSMulMeasureTheory.Lp.toTemperedDistribution_smul_eq · cited by 2Lp.toTemperedDistribution…MeasureTheory.setToFun_simpleFunc · cited by 2MeasureTheory.setToFun_si…ContinuousLinearMap.coeFn_holder · cited by 2ContinuousLinearMap.coeFn…MeasureTheory.lpTrimToLpMeasSubgroup_ae_eq · cited by 2MeasureTheory.lpTrimToLpM…MeasureTheory.lpTrimToLpMeas_ae_eq · cited by 2MeasureTheory.lpTrimToLpM…NormedAddCommGroup · cited by 15752NormedAddCommGroupMeasurableSpace · cited by 13106MeasurableSpaceMeasureTheory.Measure · cited by 10939MeasureTheory.MeasureENNReal · cited by 9879ENNRealAddSubgroup · cited by 3232AddSubgroupMeasureTheory.ae · cited by 2352MeasureTheory.aeFilter.EventuallyEq · cited by 1912Filter.EventuallyEqMeasureTheory.AEEqFun · cited by 856MeasureTheory.AEEqFunMeasureTheory.Lp · cited by 715MeasureTheory.LpMeasureTheory.MemLp · cited by 457MeasureTheory.MemLpMeasureTheory.AEEqFun.cast · cited by 380AEEqFun.castMeasureTheory.MemLp.toLp · cited by 70MemLp.toLpMeasureTheory.AEEqFun.coeFn_mk · cited by 18AEEqFun.coeFn_mkMemLp.coeFn_toLpCITED BYCITES

Cites13

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

Cited by35

Results whose statement or proof uses this declaration.