mutuallySingular_tfae — Mathlib

English

NullMeasurableSet sᶜ μ ⇔ NullMeasurableSet s μ.

Русский

NullMeasurableSet sᶜ μ эквивалентно NullMeasurableSet s μ.

LaTeX

$$$$ \\text{NullMeasurableSet }(s^{c}) \\iff \\text{NullMeasurableSet }(s). $$$$

Lean4

theorem mutuallySingular_tfae : List.TFAE [μ ⟂ₘ ν, Disjoint μ ν, Disjoint (ae μ) (ae ν)] :=
  by
  tfae_have 1 → 2
    | h => h.disjoint
  tfae_have 2 → 1
    | h => mutuallySingular_of_disjoint h
  tfae_have 1 → 3
    | h => h.disjoint_ae
  tfae_have 3 → 2
    | h => disjoint_of_disjoint_ae h
  tfae_finish

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