The Radon-Nikodym theorem and the mean convergence of Banach space valued martingales
نویسندگان
چکیده
منابع مشابه
The Radon-Nikodym Theorem for Reflexive Banach Spaces El Teorema de Radon-Nikodym para Espacios de Banach Reflexivos
In this short paper we prove the equivalence between the RadonNikodym Theorem for reflexive Banach spaces and the representability of weakly compact operators with domain L(μ).
متن کاملA Radon-nikodym Theorem for Stone Algebra Valued Measures
Introduction. Let C(S) be the ring of continuous real valued functions on a compact Hausdorff space S. Stone [5] shows that each bounded subset of C(S) has a least upper bound (in C(S)) if and only if the closure of each open subset of S is open ; in this event we call C(S) a Stone algebra. Throughout this paper C(S) is a Stone algebra. It is convenient to adjoin an object +00, not in C(S), and...
متن کاملA Reformulation of the Radon-nikodym Theorem
The Radon-Nikodym theorems of Segal and Zaanen are principally concerned with the classification of those measures p. for which any X« p. is given in the form
متن کاملON THE RADON-NiKODYM-PROPERTY AND MARTINGALE CONVERGENCE
It is well-known that there is an intimate connection between the RadonNikodym property and martingale convergence in a Banach space. This connection can be "localized" to a closed bounded convex subset of a Banach space. In this paper we are interested primarily in this connection for a bounded convex set which is not closed. If C is a bounded convex set in a locally convex space, C is said to...
متن کاملAnd Still One More Proof of the Radon-Nikodym Theorem
1. J. Burbea, Sharp inequalities for holomorphic functions, Illinois J. Math. 31 (1987) 248–264. 2. T. Carleman, Zur Theorie der Minimalflächen, Math. Z. 9 (1921) 154–160. 3. P. L. Duren, Theory of H p Spaces, Academic Press, New York, 1970; reprinted by Dover, Mineola, NY, 2000. 4. T. W. Gamelin and D. Khavinson, The isoperimetric inequality and rational approximation, this MONTHLY 96 (1989) 1...
متن کاملذخیره در منابع من
با ذخیره ی این منبع در منابع من، دسترسی به آن را برای استفاده های بعدی آسان تر کنید
ژورنال
عنوان ژورنال: Proceedings of the American Mathematical Society
سال: 1969
ISSN: 0002-9939
DOI: 10.1090/s0002-9939-1969-0238364-7