A pointwise selection principle for metric semigroup valued functions

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• 作者：Vyacheslav V. Chistyakov ; Caterina Maniscalco
• 关键词：Joint modulus of variation ; Selection principle ; Pointwise convergence ; Double sequence ; Metric semigroup
• 刊名：Journal of Mathematical Analysis and Applications
• 出版年：2008
• 出版时间：1 May 2008
• 年：2008
• 卷：341
• 期：1
• 页码：613-625
• 全文大小：197 K

文摘

Let RL&_method=retrieve&_udi=B6WK2-4R335P5-5&_mathId=mml1&_user=10&_cdi=6894&_rdoc=51&_acct=C000050221&_version=1&_userid=10&md5=535268fc23e7ba48eb72b761c36b9d2a"">, (X,d,+) be an additive commutative semigroup with metric d satisfying d(x+z,y+z)=d(x,y) for all x,y,zX, and l5"">l5&_user=10&_cdi=6894&_rdoc=51&_acct=C000050221&_version=1&_userid=10&md5=bfb64fdcf05d4d13fc9096815348b236"" title=""Click to view the MathML source"">X^T the set of all functions from T into X. If and f,gX^T, we set , where the supremum is taken over all numbers s₁,…,s_n,t₁,…,t_n from T such that s₁t₁s₂t₂s_nt_n. We prove the following pointwise selection theorem: If a sequence of functions is such that the closure in X of the set is compact for each tT, and

then it contains a subsequence which converges pointwise on T. We show by examples that this result is sharp and present two of its variants.