deterministic_comp_deterministic — Mathlib

English

For κ a kernel and hg measurable, κ ∘ₖ deterministic g hg equals comap κ g hg.

Русский

Для κ и hg измеримого вида κ ∘ₖ deterministic g hg равно comap κ g hg.

LaTeX

$$$ κ \circ_K deterministic(g, hg) = comap(κ, g, hg) $$$

Lean4

theorem deterministic_comp_deterministic (hf : Measurable f) (hg : Measurable g) :
    (deterministic g hg) ∘ₖ (deterministic f hf) = deterministic (g ∘ f) (hg.comp hf) := by ext;
  simp [comp_deterministic_eq_comap, comap_apply, deterministic_apply]

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