On U- and M-sets for series with respect to characters of compact zero-dimensional groups

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• 作者：Natalia Kholshchevnikova^b ; ^{kholshchevnikova@gmail.com" class="auth_mail" title="E-mail the corresponding author} ; Valentin Skvortsov^a ; ^{vaskvor2000@yahoo.com" class="auth_mail" title="E-mail the corresponding author}
• 关键词：Compact zero-dimensional abelian group ; Characters of a group ; U-set ; M-set ; Category problem ; Hausdorff h-measure
• 刊名：Journal of Mathematical Analysis and Applications
• 出版年：2017
• 出版时间：1 February 2017
• 年：2017
• 卷：446
• 期：1
• 页码：383-394
• 全文大小：361 K

文摘

Generalizing our previous results on Walsh system, we consider the system of characters of zero-dimensional compact abelian group with the second axiom of countability and give for the sets of uniqueness with respect to this system a solution of category problem. We also obtain a generalization of a theorem on existence for this system a perfect formulatext stixSupport mathImg" data-mathURL="/science?_ob=MathURL&_method=retrieve&_eid=1-s2.0-S0022247X16304942&_mathId=si1.gif&_user=111111111&_pii=S0022247X16304942&_rdoc=1&_issn=0022247X&md5=0d61bc21d49f89b408e0454294990811" title="Click to view the MathML source">M₀flow="scroll">M0-set whose Hausdorff h-measure equals zero.