ae_ae_eq_curry_of_prod — Mathlib

English

If f,g: α × β → γ satisfy f =ᵐ[μ × ν] g, then for μ-a.e. x, the curried functions curry f x and curry g x are equal ν-a.e.

Русский

Если f, g: α × β → γ удовлетворяют f =ᵐ[μ × ν] g, то для почти всех x по μ функции curry f x и curry g x равны ν-пAlmost everywhere.

LaTeX

$$$(f =^{\mathrm{a.e.}}_{μ \otimes ν} g) \Rightarrow \forall^{\!} x \partial μ, curry\; f\; x =^{\mathrm{a.e.}}_{ν} curry\; g\; x$$$

Lean4

theorem ae_ae_eq_curry_of_prod {γ : Type*} {f g : α × β → γ} (h : f =ᵐ[μ.prod ν] g) :
    ∀ᵐ x ∂μ, curry f x =ᵐ[ν] curry g x :=
  ae_ae_of_ae_prod h

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