id_map — Mathlib

English

Kernel.id.comap f hf = deterministic f hf; i.e., comap of the identity kernel yields a deterministic kernel.

Русский

Комап ядра идентичности даёт детерминированное ядро.

LaTeX

$$$ \operatorname{id\_comap}(f, hf) = \operatorname{deterministic}(f, hf) $$$

Lean4

@[simp]
theorem id_map {f : α → β} (hf : Measurable f) : Kernel.id.map f = deterministic f hf :=
  by
  ext
  rw [Kernel.map_apply _ hf, Kernel.deterministic_apply, Kernel.id_apply, Measure.map_dirac hf]

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