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On Multivalued Amarts

Dorota Dudek;  Wiesław Zięba — 2004

Bulletin of the Polish Academy of Sciences. Mathematics

In recent years, convergence results for multivalued functions have been developed and used in several areas of applied mathematics: mathematical economics, optimal control, mechanics, etc. The aim of this note is to give a criterion of almost sure convergence for multivalued asymptotic martingales (amarts). For every separable Banach space B the fact that every L¹-bounded B-valued martingale converges a.s. in norm to an integrable B-valued random variable (r.v.) is equivalent to the Radon-Nikodym...

Lectures of probability on Polish territory at the end of the nineteenth and early twentieth centuries

Dorota Dudek;  Wiesław Zięba — 2010

Antiquitates Mathematicae

Probability theory at the turn of the nineteenth and twentieth centuries was not treated as a branch of  mathematics, but as a part of physics. Therefore, the grounds of tasks and truthfulness rights probability often took place through experiments (which led to many erroneous statements). Following the formation and development of the theory of probability we observe some groundbreaking achievements that have enabled this area to stand on a new qualitative level. Such an achievement was undoubtedly...

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