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001 280983
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007 cr nn 008mamaa
008 150903s2009 xxu| o |||| 0|eng d
020 _a9780817646561
_99780817646561
024 7 _a10.1007/9780817646561
_2doi
035 _avtls000333599
039 9 _a201509030206
_bVLOAD
_c201404130456
_dVLOAD
_c201404092246
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_zstaff
040 _aMX-SnUAN
_bspa
_cMX-SnUAN
_erda
050 4 _aQA299.6-433
100 1 _aBenedetto, John J.
_eautor
_9306284
245 1 0 _aIntegration and Modern Analysis /
_cby John J. Benedetto, Wojciech Czaja.
264 1 _aBoston :
_bBirkhäuser Boston,
_c2009.
300 _axIx, 575 páginas 24 ilustraciones
_brecurso en línea.
336 _atexto
_btxt
_2rdacontent
337 _acomputadora
_bc
_2rdamedia
338 _arecurso en línea
_bcr
_2rdacarrier
347 _aarchivo de texto
_bPDF
_2rda
490 0 _aBirkhäuser Advanced Texts / Basler Lehrbücher
500 _aSpringer eBooks
505 0 _aClassical Real Variables -- Lebesgue Measure and General Measure Theory -- The Lebesgue Integral -- The Relationship between Differentiation and Integration on -- Spaces of Measures and the Radon–Nikodym Theorem -- Weak Convergence of Measures -- Riesz Representation Theorem -- Lebesgue Differentiation Theorem on -- Self-Similar Sets and Fractals -- Functional Analysis -- Fourier Analysis.
520 _aA paean to twentieth century analysis, this modern text has several important themes and key features which set it apart from others on the subject. A major thread throughout is the unifying influence of the concept of absolute continuity on differentiation and integration. This leads to fundamental results such as the Dieudonné–Grothendieck theorem and other intricate developments dealing with weak convergence of measures. Key Features: * Fascinating historical commentary interwoven into the exposition; * Hundreds of problems from routine to challenging; * Broad mathematical perspectives and material, e.g., in harmonic analysis and probability theory, for independent study projects; * Two significant appendices on functional analysis and Fourier analysis. Key Topics: * In-depth development of measure theory and Lebesgue integration; * Comprehensive treatment of connection between differentiation and integration, as well as complete proofs of state-of-the-art results; * Classical real variables and introduction to the role of Cantor sets, later placed in the modern setting of self-similarity and fractals; * Evolution of the Riesz representation theorem to Radon measures and distribution theory; * Deep results in modern differentiation theory; * Systematic development of weak sequential convergence inspired by theorems of Vitali, Nikodym, and Hahn–Saks; * Thorough treatment of rearrangements and maximal functions; * The relation between surface measure and Hausforff measure; * Complete presentation of Besicovich coverings and differentiation of measures. Integration and Modern Analysis will serve advanced undergraduates and graduate students, as well as professional mathematicians. It may be used in the classroom or self-study.
590 _aPara consulta fuera de la UANL se requiere clave de acceso remoto.
700 1 _aCzaja, Wojciech.
_eautor
_9306285
710 2 _aSpringerLink (Servicio en línea)
_9299170
776 0 8 _iEdición impresa:
_z9780817643065
856 4 0 _uhttp://remoto.dgb.uanl.mx/login?url=http://dx.doi.org/10.1007/978-0-8176-4656-1
_zConectar a Springer E-Books (Para consulta externa se requiere previa autentificación en Biblioteca Digital UANL)
942 _c14
999 _c280983
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