deterministic_congr — Mathlib

English

If f=g, then the deterministic kernels coincide after transporting the measurability: deterministic f hf = deterministic g (h ▸ hf).

Русский

Если f=g,Deterministic ядра совпадают после переноса измеримости.

LaTeX

$$$\deterministic f hf = \deterministic g (h \;▸\; hf)$, если $h: f=g$$$

Lean4

/-- Because of the measurability field in `Kernel.deterministic`, `rw [h]` will not rewrite
`deterministic f hf` to `deterministic g ⋯`. Instead one can do `rw [deterministic_congr h]`. -/
theorem deterministic_congr {f g : α → β} {hf : Measurable f} (h : f = g) :
    deterministic f hf = deterministic g (h ▸ hf) := by grind

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