Theorems · Theorem · functional analysis
lp.norm_tsum_le
∀ {α : Type u_3} {E : Type u_5} [inst : NormedAddCommGroup E] (f : ↥(lp (fun x => E) 1)), ‖∑' (i : α), ↑f i‖ ≤ ‖f‖- Defined in
- Mathlib.Analysis.Normed.Lp.lpSpace
- Cited by
- 0 results in Mathlib
- Foundations
- Depth 217 from the axioms · uses propext, Classical.choice, Quot.sound
- Assumes
- NormedAddCommGroup
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Cites18
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
- ENNRealstatement · cited by 9,879
- Norm.normstatement and proof · cited by 5,413
- AddSubgroupstatement · cited by 3,232
- SummationFilter.unconditionalstatement and proof · cited by 2,068
- tsumstatement and proof · cited by 1,148
- ENNReal.toRealproof · cited by 859
- Summableproof · cited by 778
- div_selfproof · cited by 237
- PreLpstatement and proof · cited by 163
- lpstatement and proof · cited by 157
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