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Titlebook: Applications of Point Set Theory in Real Analysis; A. B. Kharazishvili Book 1998 Springer Science+Business Media Dordrecht 1998 measure th

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发表于 2025-3-21 20:08:24 | 显示全部楼层 |阅读模式
期刊全称Applications of Point Set Theory in Real Analysis
影响因子2023A. B. Kharazishvili
视频videohttp://file.papertrans.cn/160/159541/159541.mp4
学科分类Mathematics and Its Applications
图书封面Titlebook: Applications of Point Set Theory in Real Analysis;  A. B. Kharazishvili Book 1998 Springer Science+Business Media Dordrecht 1998 measure th
影响因子This book is devoted to some results from the classical Point Set Theory and their applications to certain problems in mathematical analysis of the real line. Notice that various topics from this theory are presented in several books and surveys. From among the most important works devoted to Point Set Theory, let us first of all mention the excellent book by Oxtoby [83] in which a deep analogy between measure and category is discussed in detail. Further, an interesting general approach to problems concerning measure and category is developed in the well-known monograph by Morgan [79] where a fundamental concept of a category base is introduced and investigated. We also wish to mention that the monograph by Cichon, W«;glorz and the author [19] has recently been published. In that book, certain classes of subsets of the real line are studied and various cardinal­ valued functions (characteristics) closely connected with those classes are investigated. Obviously, the IT-ideal of all Lebesgue measure zero subsets of the real line and the IT-ideal of all first category subsets of the same line are extensively studied in [19], and several relatively new results concerning this topic are
Pindex Book 1998
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Martin Kaltschmitt,Karl Stampfericient conditions for the uniqueness of the standard Borel measure on .. One problem closely related to this result is also posed which seems to be interesting from the point of view of the theory of invariant measures.
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Selectors associated with subgroups of the real line,ssumptions are sufficient for the validity of Vitali’s result. In this connection, the following question arises naturally: what is the situation for other subgroups of the real line? The present section is primarily devoted to the investigation of this problem.
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of the real line. Notice that various topics from this theory are presented in several books and surveys. From among the most important works devoted to Point Set Theory, let us first of all mention the excellent book by Oxtoby [83] in which a deep analogy between measure and category is discussed
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https://doi.org/10.1007/978-3-662-47438-9d especially. It is sufficient to recall here the well-known examples of nowhere differentiable real-valued functions; examples of Lebesgue measurable real-valued functions nonintegrable on any nonempty open subinterval of .; examples of Lebesgue integrable real-valued functions with everywhere divergent Fourier series and others.
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