On the \(L^ 1_{{\mathcal F}}\) convergence for conditional Amarts
In this note we develop the relation between another type of conditional convergence of a sequence of random variables. Moreover, we generalise the theorem of convergence in \(L^ 1\) for amarts. An interesting result is stated in Theorem 4: Every uniformly \({\mathcal F}\)-integrable conditional amart converges a.s. and in \(L^ 1_{{\mathcal F}}\).
conditional convergence of a sequence of random variables
scientific article; zbMATH DE number 4060431