holderOnWith_univ — Mathlib

English

On the universal set, HolderOnWith reduces to HolderWith.

Русский

На все множество условие Холдера сводится к условию ХолдерWithoutOn.

LaTeX

$$$\\operatorname{HolderOnWith} C r f \\operatorname{univ} \\;\\iff\\; \\operatorname{HolderWith} C r f$$$

Lean4

theorem holderOnWith_univ {C r : ℝ≥0} {f : X → Y} : HolderOnWith C r f univ ↔ HolderWith C r f := by
  simp only [HolderOnWith, HolderWith, mem_univ, true_imp_iff]

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