On the Rudin-Blass Ordering of Measures

We study the Rudin-Blass (and the Rudin-Keisler) ordering on the finite additive measures on $\omega$. We propose a generalization of the notion of Q-point and selective ultrafilter to measures: Q-measures and selective measures. We show some symmetries between Q-points and Q-measures but also we show where those symmetries break up. In particular we present an example of a measure which is minimal in the sense of Rudin-Blass but which is not a Q-measure.