Theorems · Theorem · general topology
eHolderNorm_nsmul
∀ {X : Type u_1} {Y : Type u_2} [inst : MetricSpace X] [inst_1 : NormedAddCommGroup Y] {r : NNReal} {f : X → Y}
[NormedSpace ℝ Y] (n : ℕ), eHolderNorm r (n • f) = n • eHolderNorm r f- Defined in
- Mathlib.Topology.MetricSpace.HolderNorm
- Cited by
- 0 results in Mathlib
- Foundations
- Depth 210 from the axioms · uses propext, Classical.choice, Quot.sound
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Cites14
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
- Moduleproof · cited by 20,661
- NormedAddCommGroupstatement and proof · cited by 15,752
- NormedSpacestatement and proof · cited by 12,499
- AddCommMonoidproof · cited by 12,281
- ENNRealstatement · cited by 9,879
- NNRealstatement and proof · cited by 4,310
- MetricSpacestatement and proof · cited by 1,684
- ENNReal.ofNNRealproof · cited by 1,279
- nsmul_eq_mulproof · cited by 369
- Nat.cast_smul_eq_nsmulproof · cited by 110
- eHolderNormstatement and proof · cited by 16
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