comap_comp_right — Mathlib

English

Comap κ (fun a => a) measurable_id = κ, i.e., comap κ identity = κ.

Русский

Комап κ по функции, равной идентичности, даёт κ: comap κ (fun a => a) measurable_id = κ.

LaTeX

$$$ \operatorname{comap}(\kappa, (\lambda a, a), \mathrm{measurable\_id}) = \kappa $$$

Lean4

theorem comap_comp_right (κ : Kernel α β) {f : δ → γ} (hf : Measurable f) (hg : Measurable g) :
    comap κ (g ∘ f) (hg.comp hf) = (comap κ g hg).comap f hf := by ext; simp

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