toRealPositiveLinear_apply — Mathlib

English

For Λ, the real-valued positive linear map toRealPositiveLinear Λ acts on f by the prescribed formula: toRealPositiveLinear Λ f = Λ (nnrealPart f) - Λ (nnrealPart (-f)).

Русский

Для Λ действуют на f по формуле: toRealPositiveLinear Λ f = Λ (nnrealPart f) - Λ (nnrealPart (-f)).

LaTeX

$$$ toRealPositiveLinear(Λ)(f) = Λ(\mathrm{nnrealPart}(f)) - Λ(\mathrm{nnrealPart}(-f)) $$$

Lean4

theorem toRealPositiveLinear_apply {Λ : C_c(α, ℝ≥0) →ₗ[ℝ≥0] ℝ≥0} (f : C_c(α, ℝ)) :
    toRealPositiveLinear Λ f = Λ (nnrealPart f) - Λ (nnrealPart (-f)) :=
  rfl

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