pairwise_aedisjoint_of_ac — Mathlib

English

If h is a fundamental domain for G and ν ≪ μ, then the translates g₁•s and g₂•s are AEDisjoint whenever g₁ ≠ g₂, i.e., pairwise almost everywhere disjointness holds after absolute continuity.

Русский

Если h — фундаментальная область для G и ν ≪ μ, то переносы g₁•s и g₂•s параллельно AE-дисс joint, если g₁ ≠ g₂.

LaTeX

$$$\\text{Pairwise}(g_1,g_2 \\mapsto \\text{AEDisjoint } ν(g_1\\cdot s, g_2\\cdot s))$$$

Lean4

@[to_additive]
theorem pairwise_aedisjoint_of_ac {ν} (h : IsFundamentalDomain G s μ) (hν : ν ≪ μ) :
    Pairwise fun g₁ g₂ : G => AEDisjoint ν (g₁ • s) (g₂ • s) :=
  h.aedisjoint.mono fun _ _ H => hν H

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