LEADER 04355nam a22004695i 4500001 99125166619406421 005 20200630080736.0 006 m o d | 007 cr#nn#008mamaa 008 141115s2014 xxu| o |||| 0|eng d 020 1-4939-1841-9 024 7 10.1007/978-1-4939-1841-6 |2doi 035 (CKB)3710000000306065 035 (SSID)ssj0001386357 035 (PQKBManifestationID)11809737 035 (PQKBTitleCode)TC0001386357 035 (PQKBWorkID)11374004 035 (PQKB)10949356 035 (DE-He213)978-1-4939-1841-6 035 (MiAaPQ)EBC6310654 035 (MiAaPQ)EBC5594778 035 (Au-PeEL)EBL5594778 035 (OCoLC)1076232954 035 (PPN)183088654 035 (EXLCZ)993710000000306065 040 MiAaPQ |beng |erda |epn |cMiAaPQ |dMiAaPQ 041 eng 050 4 QA39.2 |b.S647 2014 072 7 PBKL |2bicssc 072 7 MAT034000 |2bisacsh 082 0 510 |223 100 1 Sohrab, Houshang H. |eauthor. |4aut |4http://id.loc.gov/vocabulary/relators/aut 245 10 Basic Real Analysis / |cby Houshang H. Sohrab. 250 2nd ed. 2014. 264 1 New York, NY : |bSpringer New York : |bImprint: Birkhäuser, |c2014. 300 1 online resource (XI, 683 p. 3 illus.) 336 text |btxt 337 computer |bc 338 online resource |bcr 500 Bibliographic Level Mode of Issuance: Monograph 546 English 505 0 Preface -- Set Theory -- Sequences and Series of Real Numbers -- Limits of Functions -- Topology of R and Continuity -- Metric Spaces -- The Derivative -- The Riemann Integral -- Sequences and Series of Functions -- Normed and Function Spaces -- The Lebesgue Integral -- Lebesgue Measure -- General Measure and Probability -- Appendix A: Construction of Real Numbers -- References -- Index. 520 This expanded second edition presents the fundamentals and touchstone results of real analysis in full rigor, but in a style that requires little prior familiarity with proofs or mathematical language. The text is a comprehensive and largely self-contained introduction to the theory of real-valued functions of a real variable. The chapters on Lebesgue measure and integral have been rewritten entirely and greatly improved. They now contain Lebesgue’s differentiation theorem as well as his versions of the Fundamental Theorem(s) of Calculus. With expanded chapters, additional problems, and an expansive solutions manual, Basic Real Analysis, Second Edition, is ideal for senior undergraduates and first-year graduate students, both as a classroom text and a self-study guide. Reviews of first edition: The book is a clear and well-structured introduction to real analysis aimed at senior undergraduate and beginning graduate students. The prerequisites are few, but a certain mathematical sophistication is required. ... The text contains carefully worked out examples which contribute motivating and helping to understand the theory. There is also an excellent selection of exercises within the text and problem sections at the end of each chapter. In fact, this textbook can serve as a source of examples and exercises in real analysis. —Zentralblatt MATH The quality of the exposition is good: strong and complete versions of theorems are preferred, and the material is organised so that all the proofs are of easily manageable length; motivational comments are helpful, and there are plenty of illustrative examples. The reader is strongly encouraged to learn by doing: exercises are sprinkled liberally throughout the text and each chapter ends with a set of problems, about 650 in all, some of which are of considerable intrinsic interest. —Mathematical Reviews [This text] introduces upper-division undergraduate or first-year graduate students to real analysis.... Problems and exercises abound; an appendix constructs the reals as the Cauchy (sequential) completion of the rationals; references are copious and judiciously chosen; and a detailed index brings up the rear. —CHOICE Reviews. 588 Description based on publisher supplied metadata and other sources. 650 0 Measure theory. 650 0 Mathematical logic. 650 14 Measure and Integration. |0https://scigraph.springernature.com/ontologies/product-market-codes/M12120 650 24 Mathematical Logic and Foundations. |0https://scigraph.springernature.com/ontologies/product-market-codes/M24005 776 |z1-4939-1840-0 906 BOOK