A Yosida-Hewitt decomposition for minitive set functions (Q812619)

A set function \(\nu:{\mathfrak A}\to \mathbb{R}\) on a \(\sigma\)-algebra is called minitive if \(\nu(A\cap B)= \min\{\nu(A), \nu(B)\}\) for all \(A,B\in{\mathfrak A}\). The author proves that a minitive set function has a unique decomposition of the form \(\nu= \nu_c+ \nu_p\) where \(\nu_c\) is \(\sigma\)-continuous and \(\nu_p\) is pure. If \({\mathfrak A}= \mathbb{P}(\mathbb{N})\), a precise description of \(\nu_c\) is given.