We introduce a new metric for weak convergence in the space $M^+(S)$ of positive finite measures on the Borel sets of a separable metric space $S$. This metric derives from a norm on the space $M(S)$ of finite rela measures on $S$. Convergence with respect to this norm is not equivalent to weak convergence for measures on $M(S)$ rather than $M^+(S)$.
A New Metric for Weak Convergence
SEMPI, Carlo
1987-01-01
Abstract
We introduce a new metric for weak convergence in the space $M^+(S)$ of positive finite measures on the Borel sets of a separable metric space $S$. This metric derives from a norm on the space $M(S)$ of finite rela measures on $S$. Convergence with respect to this norm is not equivalent to weak convergence for measures on $M(S)$ rather than $M^+(S)$.File in questo prodotto:
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