Non-archimedean function spaces and the Lebesgue dominated convergence theorem
نویسندگان
چکیده
منابع مشابه
The Lebesgue Monotone Convergence Theorem
For simplicity, we adopt the following rules: X is a non empty set, S is a σ-field of subsets of X, M is a σ-measure on S, E is an element of S, F , G are sequences of partial functions from X into R, I is a sequence of extended reals, f , g are partial functions from X to R, s1, s2, s3 are sequences of extended reals, p is an extended real number, n, m are natural numbers, x is an element of X...
متن کاملThe Sampling Theorem in Variable Lebesgue Spaces
hold. The facts above are well-known as the classical Shannon sampling theorem initially proved by Ogura [10]. Ashino and Mandai [1] generalized the sampling theorem in Lebesgue spaces L0(R) for 1 < p0 < ∞. Their generalized sampling theorem is the following. Theorem 1.1 ([1]). Let r > 0 and 1 < p0 < ∞. Then for all f ∈ L 0(R) with supp f̂ ⊂ [−rπ, rπ], we have the norm inequality C p r ‖f‖Lp0(Rn...
متن کاملcompactifications and function spaces on weighted semigruops
chapter one is devoted to a moderate discussion on preliminaries, according to our requirements. chapter two which is based on our work in (24) is devoted introducting weighted semigroups (s, w), and studying some famous function spaces on them, especially the relations between go (s, w) and other function speces are invesigated. in fact this chapter is a complement to (32). one of the main fea...
15 صفحه اولGromov-Hausdorff convergence of non-Archimedean fuzzy metric spaces
We introduce the notion of the Gromov-Hausdorff fuzzy distance between two non-Archimedean fuzzy metric spaces (in the sense of Kramosil and Michalek). Basic properties involving convergence and the fuzzy version of the completeness theorem are presented. We show that the topological properties induced by the classic Gromov-Hausdorff distance on metric spaces can be deduced from our approach.
متن کاملA New Approach to Caristi's Fixed Point Theorem on Non-Archimedean Fuzzy Metric Spaces
In the present paper, we give a new approach to Caristi's fixed pointtheorem on non-Archimedean fuzzy metric spaces. For this we define anordinary metric $d$ using the non-Archimedean fuzzy metric $M$ on a nonemptyset $X$ and we establish some relationship between $(X,d)$ and $(X,M,ast )$%. Hence, we prove our result by considering the original Caristi's fixedpoint theorem.
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 Belgian Mathematical Society - Simon Stevin
سال: 2012
ISSN: 1370-1444
DOI: 10.36045/bbms/1331153417