measure_eq_zero_iff — Mathlib

English

If f is measurable and f equals g almost everywhere, then g is measurable.

Русский

Если f измерима и f равно g почти всюду, то g измерима.

LaTeX

$$$\text{Measurable}(f) \land f =^{\mu}_{ae} g \Rightarrow \text{Measurable}(g).$$$

Lean4

theorem _root_.IsOpen.measure_eq_zero_iff (hU : IsOpen U) : μ U = 0 ↔ U = ∅ := by
  simpa only [not_lt, nonpos_iff_eq_zero, not_nonempty_iff_eq_empty] using not_congr (hU.measure_pos_iff μ)

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