000			nam a22 4500
999			_c32707 _d32707
008			240214b xxu||||| |||| 00| 0 eng d
020			_a9781071605110
082			_a515 _bDSH
100			_aDshalalow, Jewgeni H.
245			_aFoundations of abstract analysis
250			_a2nd ed.
260			_bSpringer, _aCham : _c2014
300			_axiii, 748 p. ; _c23 cm. _bill.,
365			_b3990.00 _c₹ _d01
490			_aGraduate Texts in Mathematics ; _v174
504			_aIncludes bibliographical references and index.
520			_aFoundations of Abstract Analysis is the first of a two book series offered as the second (expanded) edition to the previously published text Real Analysis. It is written for a graduate-level course on real analysis and presented in a self-contained way suitable both for classroom use and for self-study. While this book carries the rigor of advanced modern analysis texts, it elaborates the material in much greater details and therefore fills a gap between introductory level texts (with topics developed in Euclidean spaces) and advanced level texts (exclusively dealing with abstract spaces) making it accessible for a much wider interested audience. To relieve the reader of the potential overload of new words, definitions, and concepts, the book (in its unique feature) provides lists of new terms at the end of each section, in a chronological order. Difficult to understand abstract notions are preceded by informal discussions and blueprints followed by thorough details and supported by examples and figures. To further reinforce the text, hints and solutions to almost a half of more than 580 problems are provided at the end of the book, still leaving ample exercises for assignments. This volume covers topics in point-set topology and measure and integration. Prerequisites include advanced calculus, linear algebra, complex variables, and calculus based probability.
650			_aMathematical analysis
650			_aSet Theory
650			_aPoint-Set Topology
650			_aMetric spaces
650			_aAbstract Integration
650			_aMeasure Theory
650			_aPoint-Set Topology
942			_2ddc _cBK