منابع مشابه
Hartogs Type Extension Theorems
Let ∆ ⊆ C be the open unit disc and let Σ ⊆ ∆×∆ be a compact set such that K = Σ ∪ (∂∆×∆) is a connected set. It is a classical result by Hartogs that if Σ is an analytic variety over ∆ with the boundary in ∂∆×∆, then every function holomorphic in a connected neighbourhood of K extends holomorphically to a neighbourhood of ∆ × ∆. It is proved that the same conclusion holds if Σ is a ‘continuous...
متن کاملRandom Fixed Point Theorems for Measurable Multifunctions in Banach Spaces
In this paper we prove several random fixed point theorems for measurable closed and nonclosed valued multifunctions satisfying general continuity conditions. Our work extends and sharpens earlier results by Engl, Itoh and Reich. 1. Preliminaries and definitions. The study of random fixed points was initiated by the Prague school of probabilists in the fifties. Recently the interest on this sub...
متن کاملExtension Theorems without Dedekind Completeness
In the operator version of the Hahn-Banach-Kantorovich theorem, the range space Y is assumed to be Dedekind complete. Y. A. Abramovich and A. W. Wickstead improved this by assuming only the Cantor property on Y . Along the same line of reasoning, we obtained in this paper several new results of this type. We also see that assuming Cantor property on the domain spaces instead gives good results,...
متن کاملON NAKAYAMA'S EXTENSION OF THE x»<*> THEOREMS
where the a,are r fixed nonzero elements of Z, and 0<«i(a) <Ui(a) (i = 2, ■ ■ • , r), then A=Z. In [3, Theorem 11; 5; 2; l] specialized forms of (1) (e.g. cn(o) £Z, an(-a) —aEZ) are shown to imply commutativity at least for semi-simple rings. It is natural therefore to seek an extension of Nakayama's result to semi-simple rings. Since a semi-simple ring is a subdirect sum of primitive rings and...
متن کاملMeasure Extension Theorems for T0-spaces
The theme of this paper is the extension of continuous valuations on the lattice of open sets of a T0-space to Borel measures. A general extension principle is derived that provides a unified approach to a variety of extension theorems including valuations that are directed suprema of simple valuations, continuous valuations on locally compact sober spaces, and regular valuations on coherent so...
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: Journal of Mathematical Analysis and Applications
سال: 1983
ISSN: 0022-247X
DOI: 10.1016/0022-247x(83)90054-9