Theorems · Theorem · functional analysis
lp.sum_rpow_le_norm_rpow
∀ {α : Type u_3} {E : α → Type u_4} {p : ENNReal} [inst : (i : α) → NormedAddCommGroup (E i)],
0 < p.toReal → ∀ (f : ↥(lp E p)) (s : Finset α), ∑ i ∈ s, ‖↑f i‖ ^ p.toReal ≤ ‖f‖ ^ p.toReal- Defined in
- Mathlib.Analysis.Normed.Lp.lpSpace
- Cited by
- 2 results in Mathlib
- Foundations
- Depth 218 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.
Cites16
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
- Finsetstatement and proof · cited by 13,712
- ENNRealstatement and proof · cited by 9,879
- Norm.normstatement and proof · cited by 5,413
- Finset.sumstatement and proof · cited by 5,195
- AddSubgroupstatement · cited by 3,232
- ENNReal.toRealstatement and proof · cited by 859
- norm_nonnegproof · cited by 725
- PreLpstatement and proof · cited by 163
- lpstatement and proof · cited by 157
- Real.rpow_nonnegproof · cited by 111
Cited by2
Results whose statement or proof uses this declaration.
- lp.sum_rpow_le_of_tendstoproof · cited by 2
- lp.norm_monoproof · cited by 0