cond_isProbabilityMeasure — Mathlib

English

The conditional variance is unchanged when replacing a set by its measurable hull.

Русский

Условная дисперсия не изменяется при замене множества на его измеримую оболочку.

LaTeX

$$$\\mathrm{cond\\_toMeasurable\\_eq}$$$

Lean4

/-- The conditional probability measure of any finite measure on any set of positive measure
is a probability measure. -/
theorem cond_isProbabilityMeasure [IsFiniteMeasure μ] (hcs : μ s ≠ 0) : IsProbabilityMeasure μ[|s] :=
  cond_isProbabilityMeasure_of_finite hcs (measure_ne_top μ s)

Похожие утверждения