nhdsWithin_isMeasurablyGenerated — Mathlib

English

The neighborhood filter at any point is measurably generated.

Русский

filter соседствa в каждой точке измеримо порожден.

LaTeX

$$$(nhds(a)).IsMeasurablyGenerated.$$$

Lean4

/-- If `s` is a measurable set, then `𝓝[s] a` is a measurably generated filter for
each `a`. This cannot be an `instance` because it depends on a non-instance `hs : MeasurableSet s`.
-/
theorem nhdsWithin_isMeasurablyGenerated {s : Set α} (hs : MeasurableSet s) (a : α) : (𝓝[s] a).IsMeasurablyGenerated :=
  haveI := hs.principal_isMeasurablyGenerated
  Filter.inf_isMeasurablyGenerated _ _

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