Abstract
We show that if $x_n$ is optimal for the problem \[ sup\left\{\sum_{x_n}{1} log x(s)ds | \sum_0^1 (x(s)- \hat{x}(s))s^i ds = 0 , i = 0, \cdots,n , 0 \leq x \in L_1[0,1]\right\}, \] then $\frac{1}{x_n} \rightarrow \frac{1}{\hat{x}}$ weakly in $L_1$ (providing $\hat{x}$ is continuous and strictly positive). This result is a special case of a theorem for more general entropic objectives and underlying spaces.
Information
Published: 1 January 1988
First available in Project Euclid: 18 November 2014
zbMATH: 0673.41021
MathSciNet: MR1009598
Rights: Copyright © 1988, Centre for Mathematics and its Applications, Mathematical Sciences Institute, The Australian National University. This book is copyright. Apart from any fair dealing for the purpose of private study, research, criticism or review as permitted under the Copyright Act, no part may be reproduced by any process without permission. Inquiries should be made to the publisher.