000 03184nam a22004695i 4500
001 978-1-4614-5962-0
003 DE-He213
005 20140220082822.0
007 cr nn 008mamaa
008 121116s2013 xxu| s |||| 0|eng d
020 _a9781461459620
_9978-1-4614-5962-0
024 7 _a10.1007/978-1-4614-5962-0
_2doi
050 4 _aQA299.6-433
072 7 _aPBK
_2bicssc
072 7 _aMAT034000
_2bisacsh
082 0 4 _a515
_223
100 1 _aDshalalow, Jewgeni H.
_eauthor.
245 1 0 _aFoundations of Abstract Analysis
_h[electronic resource] /
_cby Jewgeni H. Dshalalow.
250 _a2nd ed. 2013.
264 1 _aNew York, NY :
_bSpringer New York :
_bImprint: Springer,
_c2013.
300 _aXIII, 748 p. 30 illus., 22 illus. in color.
_bonline resource.
336 _atext
_btxt
_2rdacontent
337 _acomputer
_bc
_2rdamedia
338 _aonline resource
_bcr
_2rdacarrier
347 _atext file
_bPDF
_2rda
505 0 _aSet-Theoretic and Algebraic Preliminaries -- Analysis of Metric Spaces -- Elements of Point-Set Topology.-Measurable Spaces and Measurable Functions -- Measures -- Integration in Abstract Spaces -- Solutions to Selected Problems -- Bibliography.-List of Symbols.-Index of Names and Terms.
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 0 _aMathematics.
650 0 _aGlobal analysis (Mathematics).
650 0 _aFunctional analysis.
650 0 _aNumerical analysis.
650 1 4 _aMathematics.
650 2 4 _aAnalysis.
650 2 4 _aFunctional Analysis.
650 2 4 _aNumerical Analysis.
710 2 _aSpringerLink (Online service)
773 0 _tSpringer eBooks
776 0 8 _iPrinted edition:
_z9781461459613
856 4 0 _uhttp://dx.doi.org/10.1007/978-1-4614-5962-0
912 _aZDB-2-SMA
999 _c95548
_d95548