eq_zero_or_isProbabilityMeasure — Mathlib

English

Let μ be a measure that is either the zero measure or a probability measure. Then μ is either the zero measure or a probability measure.

Русский

Пусть μ — мера such that μ = 0 or μ is a probability measure. Тогда μ либо нулевая мера, либо μ — вероятностная мера.

LaTeX

$$$\mu = 0 \ \lor\ \text{IsProbabilityMeasure}(\mu)$$$

Lean4

theorem eq_zero_or_isProbabilityMeasure : μ = 0 ∨ IsProbabilityMeasure μ :=
  by
  rcases IsZeroOrProbabilityMeasure.measure_univ (μ := μ) with h | h
  · apply Or.inl (measure_univ_eq_zero.mp h)
  · exact Or.inr ⟨h⟩

Похожие утверждения