Abstract:Let $\Cal A$ be an algebra and $\Cal K$ a lattice of subsets of a set $X$. We show that every content on $\Cal A$ that can be approximated by $\Cal K$ in the sense of Marczewski has an extremal extension to a $\Cal K$-regular content on the algebra generated by $\Cal A$ and $\Cal K$. Under an additional assumption, we can also prove the existence of extremal regular measure extensions.
Keywords: regular content, lattice, semicompact, sequentially dominated
AMS Subject Classification: 28A12