inducedOuterMeasure_eq_extend' — Mathlib

English

If μ(s) ≠ ∞ and ε ≠ 0, there exists t with P t and s ⊆ t such that μ(t) ≤ μ(s) + ε.

Русский

Если μ(с) ≠ ∞ и ε ≠ 0, существует t с P t и s ⊆ t с μ(t) ≤ μ(s) + ε.

LaTeX

$$$\\mu(s) \\neq \\infty \\Rightarrow \\exists t\\ (P t)\\ with\\ s \\subseteq t \\land \\mu(t) \\le \\mu(s) + \\varepsilon$$$

Lean4

theorem inducedOuterMeasure_eq_extend' {s : Set α} (hs : P s) : inducedOuterMeasure m P0 m0 s = extend m s :=
  ofFunction_eq s (fun _t => extend_mono' m_mono hs) (extend_iUnion_le_tsum_nat' PU msU)

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