LEADER 00000cam  2200493Ii 4500 
001    ocn268993106 
003    OCoLC 
005    20160518074737.4 
006    m     o  d         
007    cr cnu---unuuu 
008    081105s2001    si      ob    001 0 eng d 
019    505149559|a646768290|a764499254|a815755944 
020    9789812810656|q(electronic bk.) 
020    981281065X|q(electronic bk.) 
035    (OCoLC)268993106|z(OCoLC)505149559|z(OCoLC)646768290
       |z(OCoLC)764499254|z(OCoLC)815755944 
040    N$T|beng|epn|erda|cN$T|dOCLCQ|dUBY|dIDEBK|dE7B|dOCLCQ
       |dOCLCF|dI9W|dNLGGC|dDKDLA|dEBLCP|dDEBSZ|dOCLCQ|dYDXCP
       |dOCLCQ 
049    GTKE 
050  4 QA311|b.S88 2001eb 
082 04 515/.43|222 
100 1  Swartz, Charles,|d1938- 
245 10 Introduction to gauge integrals /|cCharles Swartz. 
246 30 Gauge integrals 
264  1 Singapore ;|aRiver Edge, NJ :|bWorld Scientific,|c[2001] 
264  4 |c©2001 
300    1 online resource (x, 157 pages) 
336    text|btxt|2rdacontent 
337    computer|bc|2rdamedia 
338    online resource|bcr|2rdacarrier 
504    Includes bibliographical references (pages 149-153) and 
       index. 
505 0  1. Introduction to the gauge or Henstock-Kurzweil integral
       -- 2. Basic properties of the gauge integral -- 3. 
       Henstock's lemma and improper integrals -- 4. The gauge 
       integral over unbounded intervals -- 5. Convergence 
       theorems -- 6. Integration over more general sets: 
       Lebesgue measure -- 7. The space of gauge integrable 
       functions -- 8. Multiple integrals and Fubini's theorem --
       9. The McShane integral. 9.1. Definition and basic 
       properties. 9.2. Convergence theorems. 9.3. Integrability 
       of products and integration by parts. 9.4. More general 
       convergence theorems. 9.5. The space of McShane integrable
       functions. 9.6. Multiple integrals and Fubini's theorem --
       10. McShane integrability is equivalent to absolute 
       Henstock-Kurzweil integrability. 
520    This book presents the Henstock/Kurzweil integral and the 
       McShane integral. These two integrals are obtained by 
       changing slightly the definition of the Riemann integral. 
       These variations lead to integrals which are much more 
       powerful than the Riemann integral. The Henstock/Kurzweil 
       integral is an unconditional integral for which the 
       fundamental theorem of calculus holds in full generality, 
       while the McShane integral is equivalent to the Lebesgue 
       integral in Euclidean spaces. A basic knowledge of 
       introductory real analysis is required of the reader, who 
       should be familiar with the fundamental properties of the 
       real numbers, convergence, series, differentiation, 
       continuity, et cetera. 
588 0  Print version record. 
650  0 Henstock-Kurzweil integral. 
650  0 McShane integral. 
650  7 MATHEMATICS|xCalculus.|2bisacsh 
650  7 MATHEMATICS|xMathematical Analysis.|2bisacsh 
650  7 Henstock-Kurzweil integral.|2fast|0(OCoLC)fst00955178 
650  7 McShane integral.|2fast|0(OCoLC)fst01013095 
655  0 Electronic books. 
776 08 |iPrint version:|aSwartz, Charles, 1938-|tIntroduction to 
       gauge integrals.|dSingapore ; River Edge, NJ : World 
       Scientific, ©2001|z9810242395|z9789810242398|w(DLC)   
       00068521|w(OCoLC)45506028 
914    ocn268993106 
994    93|bGTK