# Article

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Keywords:
linear lattice; order bounded; additive set function; quasi-measure; atomic; extension; convex set; extreme point; weakly compact
Summary:
Let $\mathfrak M$ and $\mathfrak R$ be algebras of subsets of a set $\Omega$ with $\mathfrak M\subset\mathfrak R$, and denote by $E(\mu )$ the set of all quasi-measure extensions of a given quasi-measure $\mu$ on $\mathfrak M$ to $\mathfrak R$. We give some criteria for order boundedness of $E(\mu )$ in $ba(\mathfrak R)$, in the general case as well as for atomic $\mu$. Order boundedness implies weak compactness of $E (\mu )$. We show that the converse implication holds under some assumptions on $\mathfrak M$, $\mathfrak R$ and $\mu$ or $\mu$ alone, but not in general.
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