standardBorel — Mathlib

English

The image of a measurable set under a monotone map is measurable.

Русский

Образ измеримого множества под монотонной картой измерим.

LaTeX

$$MeasurableSet (g '' t)$$

Lean4

/-- A measurable subspace of a standard Borel space is standard Borel. -/
theorem standardBorel {s : Set α} (hs : MeasurableSet s) : StandardBorelSpace s :=
  by
  obtain ⟨_, _, _, s_closed, _⟩ := hs.isClopenable'
  haveI := s_closed.polishSpace
  infer_instance

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