Theorems · Theorem · measure theory
MeasureTheory.lpNorm_sub_le_lpNorm_sub_add_lpNorm_sub
∀ {α : Type u_1} {E : Type u_2} {m : MeasurableSpace α} {p : ENNReal} {μ : MeasureTheory.Measure α}
[inst : NormedAddCommGroup E] {f g h : α → E},
MeasureTheory.MemLp f p μ →
MeasureTheory.MemLp g p μ →
1 ≤ p → MeasureTheory.lpNorm (f - h) p μ ≤ MeasureTheory.lpNorm (f - g) p μ + MeasureTheory.lpNorm (g - h) p μ- Cited by
- 0 results in Mathlib
- Foundations
- Depth 222 from the axioms · uses propext, Classical.choice, Quot.sound
- Assumes
- NormedAddCommGroup
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Cites10
Mathlib declarations this one mentions in its statement or cites explicitly in its proof. Plumbing is filtered out.
- Realstatement · 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
- MeasureTheory.MemLpstatement and proof · cited by 457
- sub_add_sub_cancelproof · cited by 56
- MeasureTheory.lpNormstatement and proof · cited by 50
- MeasureTheory.MemLp.subproof · cited by 17
- MeasureTheory.lpNorm_add_leproof · cited by 5
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