## Proceedings of the Centre for Mathematics and its Applications

### The convergence of entropic estimates for moment problems

A. S. Lewis

#### 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.

#### Article information

Dates
First available in Project Euclid: 18 November 2014