Young Measures on Topological Spaces - With Applications in Control Theory and Probability Theory (Paperback, Softcover reprint of the original 1st ed. 2004)

Classicalexamples of moreand more oscillatingreal-valued functions on a domain N ?of R are the functions u (x)=sin(nx)with x=(x ,...,x ) or the so-called n 1 1 n n+1 Rademacherfunctionson]0,1[,u (x)=r (x) = sgn(sin(2 ?x))(seelater3.1.4). n n They may appear as the gradients?v of minimizing sequences (v ) in some n n n?N variationalproblems. Intheseexamples,thefunctionu convergesinsomesenseto n ameasure on ? xR, called Young measure. In Functional Analysis formulation, this is the narrow convergence to of the image of the Lebesgue measure on ? by ? ? (?,u (?)). In the disintegrated form ( ) ,the parametrized measure n ? ??? ? captures the possible scattering of the u around ?. n Curiously if (X ) is a sequence of random variables deriving from indep- n n?N dent ones, the n-th one may appear more and more far from the k ?rst ones as 2 if it was oscillating (think of orthonormal vectors in L which converge weakly to 0). More precisely when the laws L(X ) narrowly converge to some probability n measure , it often happens that for any k and any A in the algebra generated by X ,...,X , the conditional law L(X|A) still converges to (see Chapter 9) 1 k n which means 1 ??? C (R) ?(X (?))dP(?)?? ?d b n P(A) A R or equivalently, ? denoting the image of P by ? ? (?,X (?)), n X n (1l ??)d? ?? (1l ??)d[P? ].

General

Imprint:	Springer
Country of origin:	Netherlands
Series:	Mathematics and Its Applications, 571
Release date:	December 2010
First published:	2004
Authors:	Charles Castaing • Paul Raynaud de Fitte • Michel Valadier
Dimensions:	235 x 155 x 17mm (L x W x T)
Format:	Paperback
Pages:	320
Edition:	Softcover reprint of the original 1st ed. 2004
ISBN-13:	978-90-481-6552-0
Categories:	Books > Science & Mathematics > Mathematics > Probability & statistics Books > Science & Mathematics > Mathematics > Calculus & mathematical analysis > Functional analysis Books > Science & Mathematics > Mathematics > Calculus & mathematical analysis > Integral equations Books > Science & Mathematics > Mathematics > Calculus & mathematical analysis > Calculus of variations Books > Science & Mathematics > Mathematics > Topology > General
LSN:	90-481-6552-0
Barcode:	9789048165520

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