continuous_negPart — Mathlib

English

The map f ↦ negPart f is continuous on Lp for p≥1 (as a direct corollary of the posPart continuity and the relation between negPart and posPart).

Русский

Функция f↦negPart f непрерывна на Lp при p≥1 (следствие из непрерывности posPart и связи между negPart и posPart).

LaTeX

$$$\text{Continuous}(f\mapsto\text{negPart}(f))\quad(\text{for } p≥1)$$$

Lean4

theorem continuous_negPart [Fact (1 ≤ p)] : Continuous fun f : Lp ℝ p μ => negPart f :=
  by
  unfold negPart
  exact continuous_posPart.comp continuous_neg

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