Theorems · Theorem · measure theory
MeasureTheory.lpNorm_add_le
∀ {α : Type u_1} {E : Type u_2} {m : MeasurableSpace α} {p : ENNReal} {μ : MeasureTheory.Measure α}
[inst : NormedAddCommGroup E] {f g : α → E},
MeasureTheory.MemLp f p μ →
1 ≤ p → MeasureTheory.lpNorm (f + g) p μ ≤ MeasureTheory.lpNorm f p μ + MeasureTheory.lpNorm g p μ- Cited by
- 5 results in Mathlib
- Foundations
- Depth 221 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.
Cites21
Mathlib declarations this one mentions in its statement or cites explicitly in its proof. Plumbing is filtered out.
- Realstatement and proof · cited by 25,697
- 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
- add_zeroproof · cited by 2,707
- ENNReal.toRealproof · cited by 859
- MeasureTheory.MemLpstatement and proof · cited by 457
- MeasureTheory.eLpNormproof · cited by 329
- add_sub_cancel_leftproof · cited by 198
- ENNReal.toReal_monoproof · cited by 59
- MeasureTheory.lpNormstatement and proof · cited by 50
Cited by5
Results whose statement or proof uses this declaration.
- MeasureTheory.lpNorm_add_le'proof · cited by 1
- MeasureTheory.lpNorm_le_lpNorm_add_lpNorm_subproof · cited by 0
- MeasureTheory.lpNorm_le_lpNorm_add_lpNorm_sub'proof · cited by 0
- MeasureTheory.lpNorm_sub_leproof · cited by 0
- MeasureTheory.lpNorm_sub_le_lpNorm_sub_add_lpNorm_subproof · cited by 0