equivRange — Mathlib

English

Two auxiliary measurability statements guarantee the measurable nature of the equivalence between s and f''s.

Русский

Даны два вспомогательных утверждения о измеримости, гарантирующие измеримую природу эквивалентности между s и f''s.

LaTeX

$$$ \\text{Measurable}(\\text{toFun}) \\land \\text{Measurable}(\\text{invFun}) $$$

Lean4

/-- The domain of `f` is equivalent to its range as measurable spaces,
  if `f` is a measurable embedding -/
noncomputable def equivRange (hf : MeasurableEmbedding f) : α ≃ᵐ range f :=
  (MeasurableEquiv.Set.univ _).symm.trans <|
    (hf.equivImage univ).trans <| MeasurableEquiv.cast (by rw [image_univ]) (by rw [image_univ])

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