English
If AEStronglyMeasurable X μ and not MemLp X 2 μ, then evariance X μ = ∞.
Русский
Пусть X почти surely измеримо и X ∉ L^2(μ); тогда evariance X μ = ∞.
LaTeX
$$evariance X μ = ∞ if AEStronglyMeasurable X μ and ¬ MemLp X 2 μ$$
Lean4
/-- The `ℝ`-valued variance of the real-valued random variable `X` according to the measure `μ`.
It is set to `0` if `X` has infinite variance. -/
@[scoped term_parser 1000]
public meta def «termVar[_;_]» : Lean.ParserDescr✝ :=
ParserDescr.node✝ `ProbabilityTheory.«termVar[_;_]» 1024
(ParserDescr.binary✝ `andthen
(ParserDescr.binary✝ `andthen
(ParserDescr.binary✝ `andthen
(ParserDescr.binary✝ `andthen (ParserDescr.symbol✝ "Var[") (ParserDescr.cat✝ `term 0))
(ParserDescr.symbol✝ "; "))
(ParserDescr.cat✝ `term 0))
(ParserDescr.symbol✝ "]"))
