Abstract
In this paper martingales of statistical Bochner integrable functions with values in a Banach space are treated. In particular we have arrived some results for martingales and backwards martingales.
Highlights
The study of probability theory in abstract spaces became possible with the introduction of integration theories in such spaces
Much of the work on Banach spaces done in the 1930’s resulted from investigating how much of real variable theory might be extended to functions taking values in such spaces
In the 1960’s, the theory of martingales of real or complex random variables has been extended by various authors to random variables taking values in a Banach space
Summary
The study of probability theory in abstract spaces became possible with the introduction of integration theories in such spaces. In this paper we treat convergence theorems for martingales of statistical Bochnerintegrable functions. Holds for all k that is a.a.k. The vectorial sequence x is statistically convergent to the vector L of a vectorial normed space if for each 0 lim 1 | k n : ||x L || | 0 n n
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