ProbabilityMeasure — Mathlib

English

For a sequence of probability measures μ_s, if f is bounded, continuous and nonnegative, the lintegral inequality holds: ∫ f dμ ≤ liminf ∫ f dμ_s.

Русский

Для ограниченной непрерывной неотрицательной функции f выполняется неравенство: ∫ f dμ ≤ liminf ∫ f dμ_s.

LaTeX

$$$f \\text{ bounded, continuous};\\; (\\forall G\\text{ open}, μ(G) ≤ \\liminf_i μ_s(i,G)) \\Rightarrow \\int f\,dμ ≤ \\liminf_i \\int f\,dμ_s(i)$$$

Lean4

/-- Probability measures are defined as the subtype of measures that have the property of being
probability measures (i.e., their total mass is one). -/
def ProbabilityMeasure (Ω : Type*) [MeasurableSpace Ω] : Type _ :=
  { μ : Measure Ω // IsProbabilityMeasure μ }

Похожие утверждения