Young Measures on Topological Spaces: With Applications in Control Theory and Probability Theory. Questo articolo non è disponibile.
Lingua: inglese
Editore: Springer, 2010
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Codice articolo 118199
- Titolo
- Young Measures on Topological Spaces: With Applications in Control Theory and Probability Theory
- Autore
- Charles Castaing; Paul Raynaud de Fitte; Michel Valadier
- Editore
- Springer
- Anno di pubblicazione
- 2010
- Condizione
- New
- Tipo di libro
- Book
- Rilegatura
- Soft cover
- Lingua
- inglese
- ISBN 10
- 9048165520
- ISBN 13
- 9789048165520
Classicalexamples of moreand more oscillatingrealvalued 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 µ on ? ×R, called Young measure. In Functional Analysis formulation, this is the narrow convergence to µ of the image of the Lebesgue measure on ? by ? ? (?,u (?)). In the disintegrated form (µ ) ,the parametrized measure µ 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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Recensione
From the reviews:
"This book presents a wealth of results on Young measures on topological spaces in a very general framework. It is very likely that it will become the reference and starting point for any further developments in the field." (Georg K. Dolzmann, Mathematical Reviews, 2005k)
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