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- 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.
Cites13
Mathlib declarations this one mentions in its statement or cites explicitly in its proof. Plumbing is filtered out.
- NormedAddCommGroupstatement and proof · cited by 15,752
- MeasurableSpacestatement and proof · cited by 13,106
- MeasureTheory.Measurestatement and proof · cited by 10,939
- ENNRealstatement and proof · cited by 9,879
- AddSubgroupstatement · cited by 3,232
- MeasureTheory.aestatement · cited by 2,352
- Filter.EventuallyEqstatement · cited by 1,912
- MeasureTheory.AEEqFunstatement · cited by 856
- MeasureTheory.Lpstatement · cited by 715
- MeasureTheory.MemLpstatement and proof · cited by 457
- MeasureTheory.AEEqFun.caststatement · cited by 380
- MeasureTheory.MemLp.toLpstatement · cited by 70
Cited by35
Results whose statement or proof uses this declaration.
- MeasureTheory.indicatorConstLp_coeFnproof · cited by 15
- MeasureTheory.Lp.norm_toLpproof · cited by 7
- MeasureTheory.lpMeasSubgroupToLpTrim_ae_eqproof · cited by 6
- SchwartzMap.coeFn_toLpproof · cited by 5
- ProbabilityTheory.uncenteredCovarianceBilinDual_applyproof · cited by 4
- MeasureTheory.Lp.edist_toLp_toLpproof · cited by 4
- integral_withDensity_eq_integral_smulproof · cited by 4
- ContinuousLinearMap.comp_memLp'proof · cited by 3
- MeasureTheory.integral_condExpL2_eqproof · cited by 3
- MeasureTheory.Lp.coeFn_lpSMulproof · cited by 2
- MeasureTheory.Lp.toTemperedDistribution_smul_eqproof · cited by 2
- MeasureTheory.setToFun_simpleFuncproof · cited by 2