Let a sequence of r.v. $X_n(\omega )\overset{L^2}{\rightarrow}X(\omega )$ and $g(x)$ a continuous bounded function.
Is this implies ,and if yes can you please give the prove, that $g(X_n(\omega ))\overset{a.s.}{\rightarrow}g(X(\omega ))$
2026-02-26 12:39:28.1772109568
If $X_n(\omega )\overset{L^2}{\rightarrow}X(\omega )$ and g(x) is continuous and bounded so $g(X_n(\omega ))\overset{a.s.}{\rightarrow}g(X(\omega ))$
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