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- 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.
Cites8
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
- sub_eq_add_negproof · cited by 1,023
- MeasureTheory.MemLpstatement and proof · cited by 457
- MeasureTheory.MemLp.addproof · cited by 24
- MeasureTheory.MemLp.negproof · cited by 12
Cited by17
Results whose statement or proof uses this declaration.
- MeasureTheory.lpNorm_add_leproof · cited by 5
- ProbabilityTheory.covariance_add_leftproof · cited by 4
- ProbabilityTheory.evariance_lt_topproof · cited by 3
- MeasureTheory.unifIntegrable_of_tendsto_Lpproof · cited by 2
- ProbabilityTheory.variance_add_constproof · cited by 2
- ProbabilityTheory.covarianceBilinDual_applyproof · cited by 2
- ProbabilityTheory.HasIndepIncrements.isPreBrownianReal_of_hasLawproof · cited by 1
- MeasureTheory.MemLp.exists_boundedContinuous_integral_rpow_sub_leproof · cited by 1
- MeasureTheory.MemLp.exists_hasCompactSupport_integral_rpow_sub_leproof · cited by 1
- ProbabilityTheory.IndepFun.hasGaussianLaw_sub_of_subproof · cited by 1
- ProbabilityTheory.covariance_sub_subproof · cited by 1
- MeasureTheory.Lp.tendsto_Lp_iff_tendsto_eLpNorm''proof · cited by 0