Convergence of Banach valued stochastic processes of Pettis and McShane integrable functions
نویسنده
چکیده
It is shown that if (Xn)n is a Bochner integrable stochastic process taking values in a Banach lattice E, the convergence of f(Xn) to f(X) where f is in a total subset of E∗ implies the a.s. convergence. For any Banach space E-valued stochastic process of Pettis integrable strongly measurable functions (Xn)n, the convergence of f(Xn) to f(X) for each f in a total subset of E∗ implies the convergence in the Pettis norm. Also convergence theorems of Mc-Shane integrable martingales are given.
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