LEADER 04183nam  22007332  450 
001 9910780072803321
005 20151005020624.0
010   $a1-107-11701-1
010   $a1-280-42056-1
010   $a9786610420568
010   $a0-511-17383-0
010   $a0-511-15307-4
010   $a0-511-30334-3
010   $a0-511-54301-8
010   $a0-511-05220-0
035   $a(CKB)111056485650378
035   $a(EBL)157035
035   $a(OCoLC)191035670
035   $a(SSID)ssj0000102917
035   $a(PQKBManifestationID)11132807
035   $a(PQKBTitleCode)TC0000102917
035   $a(PQKBWorkID)10060664
035   $a(PQKB)10863446
035   $a(UkCbUP)CR9780511543012
035   $a(MiAaPQ)EBC157035
035   $a(Au-PeEL)EBL157035
035   $a(CaPaEBR)ebr10014950
035   $a(CaONFJC)MIL42056
035   $a(PPN)261331604
035   $a(EXLCZ)99111056485650378
100   $a20090505d2001||||  uy|            0
101 0 $aeng
135   $aur|||||||||||
181   $ctxt$2rdacontent
182   $cc$2rdamedia
183   $acr$2rdacarrier
200 10$aAnalysis in integer and fractional dimensions /$fRon Blei$b[electronic resource]
210  1$aCambridge :$cCambridge University Press,$d2001.
215   $a1 online resource (xix, 556 pages) $cdigital, PDF file(s)
225 1 $aCambridge studies in advanced mathematics ;$v71
300   $aTitle from publisher's bibliographic system (viewed on 05 Oct 2015).
311   $a0-511-01266-7 
311   $a0-521-65084-4 
320   $aIncludes bibliographical references (p. 534-545) and index.
327   $aPart I: A prologue: mostly historical -- Part II: Three classical inequalities -- Part III: A fourth inequality -- Part IV: Elementary properties of the Frechet variation- an introduction to tensor products -- Part V: The Grothendieck factorization theorem -- Part VI: An introduction to multidimensional measure theory -- Part VII: An introduction to harmonic analysis -- Part VIII: Multilinear extensions of the Grothendieck inequality (via "V"(2)-uniformizability) -- Part IX: Product Fre?chet measures -- Part X: Brownian motion and the Wiener process -- Part XI: Integrators -- Part XII: A '3/2-dimensional' Cartesian product -- Part XIII: Fractional cartesian products and cominatorial dimension -- Part XIV: The last chapter: leads and loose ends.
330   $aThis book provides a thorough and self-contained study of interdependence and complexity in settings of functional analysis, harmonic analysis and stochastic analysis. It focuses on 'dimension' as a basic counter of degrees of freedom, leading to precise relations between combinatorial measurements and various indices originating from the classical inequalities of Khintchin, Littlewood and Grothendieck. The basic concepts of fractional Cartesian products and combinatorial dimension are introduced and linked to scales calibrated by harmonic-analytic and stochastic measurements. Topics include the (two-dimensional) Grothendieck inequality and its extensions to higher dimensions, stochastic models of Brownian motion, degrees of randomness and Frechet measures in stochastic analysis. This book is primarily aimed at graduate students specialising in harmonic analysis, functional analysis or probability theory. It contains many exercises and is suitable to be used as a textbook. It is also of interest to scientists from other disciplines, including computer scientists, physicists, statisticians, biologists and economists.
410  0$aCambridge studies in advanced mathematics ;$v71.
517 3 $aAnalysis in Integer & Fractional Dimensions
606   $aHarmonic analysis
606   $aFunctional analysis
606   $aProbabilities
606   $aInequalities (Mathematics)
615  0$aHarmonic analysis.
615  0$aFunctional analysis.
615  0$aProbabilities.
615  0$aInequalities (Mathematics)
676   $a515/.2433
700   $aBlei$b R. C$g(Ron C.),$066443
801  0$bUkCbUP
801  1$bUkCbUP
906   $aBOOK
912   $a9910780072803321
996   $aAnalysis in integer and fractional dimensions$9377744
997   $aUNINA