Some types of vector measures (Q1321632)

Let \(T\) be a locally compact Hausdorff space. \textit{R. A. Johnson} [Proc. Am. Math. Soc. 22, 94--99 (1969; Zbl 0176.00802)] has proved that every positive Borel measure \(\mu\) on \(T\) can be decomposed into the form \(\mu= \mu_1+\mu_2\), where \(\mu_1\) is a monogenic and \(\mu_2\) an antimonogenic positive Borel measure. Hereby \(\mu_1\) is called monogenic if \(\mu_1\) is the only positive Borel measure which coincides with \(\mu_ 1\) on the Baire sets. The author of the paper under review tries to transfer Johnson's theorem to the context of vector measures. But that doesn't make sense: Obviously, there is no locally compact Hausdorff space admitting (in the terminology of the author) monogenic as well as non-monogenic real Borel measures.