相關主題
商品描述
This book offers several topics of mathematical analysis which are closely connected with significant properties of real-valued functions of various types (such as semi-continuous functions, monotone functions, convex functions, measurable functions, additive and linear functionals, etc.). Alongside with fairly traditional themes of real analysis and classical measure theory, more profound questions are thoroughly discussed in the book - appropriate extensions and restrictions of functions, oscillation functions and their characterization, discontinuous functions on resolvable topological spaces, pointwise limits of finite sums of periodic functions, some general results on invariant and quasi-invariant measures, the structure of non-measurable sets and functions, the Baire property of functions on topological spaces and its connections with measurability properties of functions, logical and set-theoretical aspects of the behavior of real-valued functions.
商品描述(中文翻譯)
本書提供了幾個數學分析的主題，這些主題與各類型實值函數的重要性質密切相關（例如半連續函數、單調函數、凸函數、可測函數、加法和線性泛函等）。除了相當傳統的實分析和古典測度理論主題外，本書還深入探討了更深層次的問題——函數的適當擴展和限制、振盪函數及其特徵、在可解拓撲空間上的不連續函數、周期函數有限和的點極限、關於不變和準不變測度的一些一般結果、不可測集合和函數的結構、拓撲空間上函數的Baire性質及其與函數可測性質的關聯、實值函數行為的邏輯和集合論方面。
作者簡介
Alexander Kharazishvili is a chief researcher at the A. Razmadze Mathematical Institute of Tbilisi State University and a member of the Georgian National Academy of Sciences. His research interests mainly concern real analysis and measure theory, mostly with various properties of real-valued functions such as topological, algebraic, measure-theoretical, etc. He has more than 300 scientific publications and is the author of the book "Strange Functions in Real Analysis", published by CRC Press. The third edition of this book was published in 2018.
作者簡介(中文翻譯)
亞歷山大·哈拉齊什維利是第比利斯國立大學A. Razmadze數學研究所的首席研究員，也是喬治亞國家科學院的成員。他的研究興趣主要集中在實分析和測度理論，特別是各種實值函數的性質，如拓撲性、代數性、測度理論等。他擁有超過300篇科學出版物，並且是由CRC Press出版的《實分析中的奇異函數》一書的作者。該書的第三版於2018年出版。
