comp_eq_comp_const_apply — Mathlib

English

Composition of a measure with kernels is associative: κ ∘ₘ μ composed with η equals (η ∘ κ) ∘ₘ μ.

Русский

Компоновка меры с ядрами ассоциативна: κ ∘ₘ μ слагается с η как (η ∘ κ) ∘ₘ μ.

LaTeX

$$κ ∘ₘ μ = (η ∘ₖ κ) ∘ₘ μ$$

Lean4

/-- This lemma allows to rewrite the composition of a measure and a kernel as the composition
of two kernels, which allows to transfer properties of `∘ₖ` to `∘ₘ`. -/
theorem comp_eq_comp_const_apply : κ ∘ₘ μ = (κ ∘ₖ (Kernel.const Unit μ)) () := by
  rw [Kernel.comp_apply, Kernel.const_apply]

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