Young Measures on Topological Spaces : With Applications in Control Theory and Probability Theory
Language: English
Published by Springer, 2010
- Softcover
- New
Seller: AHA-BUCH GmbH, Einbeck, GermanyAHA-BUCH GmbH
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Druck auf Anfrage Neuware - Printed after ordering - 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 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 ].…
Seller Inventory # 9789048165520
- Title
- Young Measures on Topological Spaces : With Applications in Control Theory and Probability Theory
- Author
- Charles Castaing
- Publisher
- Springer
- Publication year
- 2010
- Condition
- Neu
- Binding
- Taschenbuch
- Language
- English
- ISBN 10
- 9048165520
- ISBN 13
- 9789048165520
- Item weight
- 511 grams
- Dimensions
- 235x155x19 mm
"Synopsis" may belong to another edition of this title.
Review
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)
"About the title" may belong to another edition of this title.
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