Theorems · Theorem · functional analysis
MeasureTheory.MemLp.neg
∀ {α : Type u_1} {E : Type u_4} {m0 : MeasurableSpace α} {p : ENNReal} {μ : MeasureTheory.Measure α}
[inst : NormedAddCommGroup E] {f : α → E}, MeasureTheory.MemLp f p μ → MeasureTheory.MemLp (-f) p μ- Cited by
- 12 results in Mathlib
- Foundations
- Depth 204 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
- Top.topproof · cited by 9,680
- MeasureTheory.MemLpstatement and proof · cited by 457
- MeasureTheory.eLpNorm_negproof · cited by 15
- MeasureTheory.AEStronglyMeasurable.negproof · cited by 11
Cited by12
Results whose statement or proof uses this declaration.
- MeasureTheory.MemLp.subproof · cited by 17
- MeasureTheory.SimpleFunc.memLp_approxOnproof · cited by 3
- ProbabilityTheory.variance_subproof · cited by 2
- MeasureTheory.MemLp.absproof · cited by 2
- ProbabilityTheory.covariance_sub_leftproof · cited by 2
- ProbabilityTheory.covariance_sub_rightproof · cited by 2
- MeasureTheory.memLp_neg_iffproof · cited by 0
- MeasureTheory.lpNorm_le_add_lpNorm_addproof · cited by 0
- MeasureTheory.lpNorm_le_lpNorm_add_lpNorm_subproof · cited by 0
- MeasureTheory.MemLp.neg_partproof · cited by 0
- MeasureTheory.MemLp.toLp_negstatement · cited by 0
- MeasureTheory.Lp.simpleFunc.toLp_negstatement · cited by 0