Erratum to ‘‘Martingales of strongly measurable Pettis integrable functions”
نویسندگان
چکیده
منابع مشابه
Convergence of Banach valued stochastic processes of Pettis and McShane integrable functions
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 conver...
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For an arbitrary in nite-dimensional Banach space X, we construct examples of strongly-measurable X-valued Pettis integrable functions whose indefinite Pettis integrals are nowhere weakly di erentiable; thus, for these functions the Lebesgue Di erentiation Theorem fails rather spectacularly. We also relate the degree of nondi erentiability of the inde nite Pettis integral to the cotype of X, fr...
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In this paper, we introduce the Denjoy-Pettis integral of set-valued mappings and investigate some properties of the set-valued Denjoy-Pettis integral. Finally we obtain the Dominated Convergence Theorem and Monotone Convergence Theorem for set-valued DenjoyPettis integrable mappings.
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A linear and continuous operator between Banach spaces is said to be absolutely summing if it maps unconditionally convergent series into absolutely convergent series. Moreover, it improves properties of stochastic processes. Indeed, N.Ghoussoub in [7] proved that an operator is absolutely summing if and only if it maps amarts (asymptotic martingales) into uniform amarts. In this paper we go a ...
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ژورنال
عنوان ژورنال: Transactions of the American Mathematical Society
سال: 1973
ISSN: 0002-9947
DOI: 10.1090/s0002-9947-1973-0319263-4