Absolute continuity and weak compactness
نویسندگان
چکیده
منابع مشابه
Dependent Choices and Weak Compactness
We work in set-theory without the Axiom of Choice ZF. We prove that the principle of Dependent Choices (DC) implies that the closed unit ball of a uniformly convex Banach space is weakly compact, and in particular, that the closed unit ball of a Hilbert space is weakly compact. These statements are not provable in ZF, and the latter statement does not imply DC. Furthermore, DC does not imply th...
متن کاملSmoothness and Weak* Sequential Compactness
If a Banach space E has an equivalent smooth norm, then every bounded sequence in E* has a weak* converging subsequence. Generalizations of this result are obtained.
متن کاملCharacterizing Continuity by Preserving Compactness and Connectedness
Let us call a function f from a space X into a space Y preserving if the image of every compact subspace of X is compact in Y and the image of every connected subspace of X is connected in Y . By elementary theorems a continuous function is always preserving. Evelyn R. McMillan [6] proved in 1970 that if X is Hausdorff, locally connected and Frèchet, Y is Hausdorff, then the converse is also tr...
متن کاملPointwise Differentiability and Absolute Continuity
This paper is concerned with the relationships between L differentiability and Sobolev functions. It is shown that if / is a Sobolev function with weak derivatives up to order k in L , and 0 s / s k, then / has an L derivative of order / everywhere except for a set which is small in the sense of an appropriate capacity. It is also shown that if a function has an 2V derivative P everywhere excep...
متن کاملA Weak Grothendieck Compactness Principle
The Grothendieck compactness principle states that every norm compact subset of a Banach space is contained in the closed convex hull of a norm null sequence. In this article, an analogue of the Grothendieck compactness principle is considered when the norm topology of a Banach space is replaced by its weak topology. It is shown that every weakly compact subset of a Banach space is contained in...
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: Bulletin of the American Mathematical Society
سال: 1975
ISSN: 0002-9904
DOI: 10.1090/s0002-9904-1975-13917-6