Isbn: 9781402019630 - young measures on topological spaces: with applications in control theory and probability theory (mathematics and its applications, 571, band 571) (12 Ergebnisse)

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Hardback. Zustand: New. 2004 ed. 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? ].…

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Hardback. Zustand: New. 2004 ed. 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? ].…

Zustand: New. Print on Demand pp. 336 52:B&W 6.14 x 9.21in or 234 x 156mm (Royal 8vo) Case Laminate on White w/Gloss Lam.

Gebunden. Zustand: New. Dieser Artikel ist ein Print on Demand Artikel und wird nach Ihrer Bestellung fuer Sie gedruckt. Provides a unified presentation of the theory, together with new results and applications in various fieldsPreface. Generalities, Preliminary results. Young Measures, the four Stable Topologies: S, M, N, W. Convergence in Probability of Young Measures (.…

Zustand: New. PRINT ON DEMAND pp. 336.