sigmaFiniteSetWRT — Mathlib

English

Definition: sigmaFiniteSetWRT(μ, ν) is a measurable set S such that μ|S is sigma-finite and for every t ⊆ S^c with ν(t) ≠ 0, μ(t) = ∞.

Русский

Определение: sigmaFiniteSetWRT(μ, ν) — измеримое множество S такое, что ограничение μ на S сигма-конечно и для любого t ⊆ S^c, если ν(t) ≠ 0, то μ(t) = ∞.

LaTeX

$$$\text{sigmaFiniteSetWRT}(μ,ν) = S$ где $S$ удовлетворяет указngu условиям$$

Lean4

/-- A measurable set such that `μ.restrict (μ.sigmaFiniteSetWRT ν)` is sigma-finite and for all
measurable sets `t ⊆ sᶜ`, either `ν t = 0` or `μ t = ∞`. -/
def sigmaFiniteSetWRT (μ ν : Measure α) : Set α :=
  if h : ∃ s : Set α, MeasurableSet s ∧ SigmaFinite (μ.restrict s) ∧ (∀ t, t ⊆ sᶜ → ν t ≠ 0 → μ t = ∞) then h.choose
  else ∅

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