03039nam 2200589Ia 450 991081089410332120240404153759.01-281-95631-79786611956318981-281-065-X(CKB)1000000000538105(StDuBDS)AH24685565(SSID)ssj0000182601(PQKBManifestationID)11178056(PQKBTitleCode)TC0000182601(PQKBWorkID)10172683(PQKB)10037072(MiAaPQ)EBC1681611(WSP)00004361(Au-PeEL)EBL1681611(CaPaEBR)ebr10255504(CaONFJC)MIL195631(OCoLC)815755944(EXLCZ)99100000000053810520001122d2001 uy 0engur|||||||||||txtccrIntroduction to gauge integrals /Charles Swartz1st ed.Singapore ;River Edge, N.J. World Scientificc20011 online resource (150p.) Bibliographic Level Mode of Issuance: Monograph981-02-4239-5 Includes bibliographical references (p. 149-153) and index.Introduction to the gauge or Henstock-Kurzweil integral; basic properties of the gauge integral; Henstock's Lemma and improper integrals; the gauge integral over unbounded intervals; convergence theorems; integration over more general sets -Lebesgue measure; the space of gauge integrable functions; multiple integrals and Fubini's theorem; the McShane integral; McShane integrability is equivalent to absolute Henstock-Kurzweil integrability.A presentation of the Henstock/Kurzweil integral and the McShane integral. These two integrals are obtained by changing slightly the definition of the Riemann integral. A basic knowledge of introductory real analysis is required of the reader.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, etc.Henstock-Kurzweil integralCalculusHenstock-Kurzweil integral.Calculus.515/.43Swartz Charles1938-54079MiAaPQMiAaPQMiAaPQBOOK9910810894103321Introduction to gauge integrals4075185UNINA