A new necessary and sufficient condition for the Egoroff theorem in non-additive measure theory

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• 作者：Masayuki Takahashi ; ^{masayuki@fz.dis.titech.ac.jp" class="auth_mail} ; Toshiaki Murofushi ; Shin Asahina
• 关键词：Non-additive measures ; Almost everywhere convergence ; Almost uniform convergence
• 刊名：Fuzzy Sets and Systems
• 出版年：1 June, 2014
• 年：2014
• 卷：244
• 期：Complete
• 页码：34-40
• 全文大小：227 K

文摘

This paper shows that a newly defined condition, called condition (M), is a necessary and sufficient condition for the Egoroff theorem in non-additive measure theory. The existing necessary and sufficient conditions for the Egoroff theorem are described by a doubly-indexed sequence of measurable sets, while condition (M) is described by a singly-indexed sequence of measurable sets.