realToNNReal — Mathlib

English

If f: NNReal → NNReal is continuous on t and s is such that Real.toNNReal maps s into t, then the composition x ↦ f(x.toNNReal) as a function ℝ → ℝ is continuous on s.

Русский

Если f: NNReal → NNReal непрерывно на t, и s удовлетворяет, что Real.toNNReal отображает s в t, тогда композиция x ↦ f(x.toNNReal) непрерывна на s.

LaTeX

$$$ContinuousOn (\\lambda x, f(x.toNNReal))\ \text{ on } s$$$

Lean4

/-- `Real.toNNReal` bundled as a continuous map for convenience. -/
@[simps -fullyApplied]
noncomputable def _root_.ContinuousMap.realToNNReal : C(ℝ, ℝ≥0) :=
  .mk Real.toNNReal continuous_real_toNNReal

Похожие утверждения