000 04936cam a2200565Ki 4500
001 9780429462153
003 FlBoTFG
005 20220531132532.0
006 m o d
007 cr cnu---unuuu
008 181018s2018 flu ob 001 0 eng d
040 _aOCoLC-P
_beng
_erda
_epn
_cOCoLC-P
020 _a9780429462153
_q(electronic bk.)
020 _a0429462158
_q(electronic bk.)
020 _a9780429868825
_q(electronic bk. : EPUB)
020 _a0429868820
_q(electronic bk. : EPUB)
020 _a9780429868818
_q(electronic bk. : Mobipocket)
020 _a0429868812
_q(electronic bk. : Mobipocket)
020 _z9781138616370
020 _a9780429868832
020 _a0429868839
020 _z1138616370
035 _a(OCoLC)1057341616
035 _a(OCoLC-P)1057341616
050 4 _aQA274.5
_b.W69 2018eb
072 7 _aMAT
_x003000
_2bisacsh
072 7 _aMAT
_x029000
_2bisacsh
082 0 4 _a519.2/36
_223
100 1 _aWoyczyński, W. A.
_q(Wojbor Andrzej),
_d1943-
_eauthor.
245 1 0 _aGeometry and martingales in Banach spaces /
_cWojbor A. Woyczynski (Case Western Reserve University).
264 1 _aBoca Raton, Florida :
_bCRC Press,
_c[2018]
300 _a1 online resource.
336 _atext
_btxt
_2rdacontent
337 _acomputer
_bc
_2rdamedia
338 _aonline resource
_bcr
_2rdacarrier
520 _a"This book provides a compact exposition of the results explaining the interrelations existing between the metric geometry of Banach spaces and the theory of martingales with values in those Banach spaces"--
_cProvided by publisher.
505 0 _aCover; Half title; Title; Copyrights; Contents; Introduction; Notation; 1 Preliminaries: Probability and geometry in Banach spaces; 1.1 Random vectors in Banach spaces; 1.2 Random series in Banach spaces; 1.3 Basic geometry of Banach spaces; 1.4 Spaces with invariant under spreading norms which are finitely representable in a given space; 1.5 Absolutely summing operators and factorization results; 2 Dentability, Radon-Nikodym Theorem, and Mar-tingale Convergence Theorem; 2.1 Dentability; 2.2 Dentability versus Radon-Nikodym property, and martingale convergence
505 8 _a2.3 Dentability and submartingales in Banach lattices and lattice bounded operators3 Uniform Convexity and Uniform Smoothness; 3.1 Basic concepts; 3.2 Martingales in uniformly smooth and uniformly convex spaces; 3.3 General concept of super-property; 3.4 Martingales in super-reflexive Banach spaces; 4 Spaces that do not contain c0; 4.1 Boundedness and convergence of random series; 4.2 Pre-Gaussian random vectors; 5 Cotypes of Banach spaces; 5.1 Infracotypes of Banach spaces; 5.2 Spaces of Rademacher cotype; 5.3 Local structure of spaces of cotype q; 5.4 Operators in spaces of cotype q
505 8 _a5.5 Random series and law of large numbers5.6 Central limit theorem, law of the iterated loga-rithm, and infinitely divisible distributions; 6 Spaces of Rademacher and stable types; 6.1 Infratypes of Banach spaces; 6.2 Banach spaces of Rademacher-type p; 6.3 Local structures of spaces of Rademacher-type p . .; 6.4 Operators on Banach spaces of Rademacher-type p; 6.5 Banach spaces of stable-type p and their local structures; 6.6 Operators on spaces of stable-type p; 6.7 Extented basic inequalities and series of random vectors in spaces of type p
505 8 _a6.8 Strong laws of large numbers and asymptotic be-havior of random sums in spaces of Rademacher-type p6.9 Weak and strong laws of large numbers in spaces of stable-type p; 6.10 Random integrals, convergence of infinitely divisi-ble measures and the central limit theorem; 7 Spaces of type 2; 7.1 Additional properties of spaces of type 2; 7.2 Gaussian random vectors; 7.3 Kolmogorov's inequality and three-series theorem .; 7.4 Central limit theorem; 7.5 Law of iterated logarithm; 7.6 Spaces of type 2 and cotype 2; 8 Beck convexity
505 8 _a8.1 General definitions and properties and their rela-tionship to types of Banach spaces8.2 Local structure of B-convex spaces and preservation of B-convexity under standard operations; 8.3 Banach lattices and reflexivity of B-convex spaces; 8.4 Classical weak and strong laws of large numbers in B-convex spaces; 8.5 Laws of large numbers for weighted sums and not necessarily independent summands; 8.6 Ergodic properties of B-convex spaces; 8.7 Trees in B-convex spaces; 9 Marcinkiewicz-Zygmund Theorem in Banach spaces; 9.1 Preliminaries
588 _aOCLC-licensed vendor bibliographic record.
650 0 _aMartingales (Mathematics)
650 0 _aGeometric analysis.
650 0 _aBanach spaces.
650 7 _aMATHEMATICS / Applied
_2bisacsh
650 7 _aMATHEMATICS / Probability & Statistics / General
_2bisacsh
856 4 0 _3Taylor & Francis
_uhttps://www.taylorfrancis.com/books/9780429462153
856 4 2 _3OCLC metadata license agreement
_uhttp://www.oclc.org/content/dam/oclc/forms/terms/vbrl-201703.pdf
999 _c73657
_d73657