sigmaFinite — Mathlib

English

If μ.restrict s is sigma-finite, then μ.restrict (s ∩ t) is sigma-finite.

Русский

Если μ.restrict s сигма-конечна, то μ.restrict (s ∩ t) сигма-конечна.

LaTeX

$$instance [SigmaFinite (μ.restrict s)] : SigmaFinite (μ.restrict (s ∩ t))$$

Lean4

instance sigmaFinite (μ ν : Measure α) [SigmaFinite μ] [SigmaFinite ν] : SigmaFinite (μ + ν) :=
  by
  rw [← sum_cond]
  refine @sum.sigmaFinite _ _ _ _ _ (Bool.rec ?_ ?_) <;> simpa

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