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arXiv · 2504.14678

On the Rudin-Blass Ordering of Measures

Piotr Borodulin-Nadzieja·Arturo Martínez-Celis·Adam Morawski·Jadwiga Świerczyńska
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Abstract

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.

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Piotr Borodulin-Nadzieja, Arturo Martínez-Celis, Adam Morawski, Jadwiga Świerczyńska. 2025-04-20. On the Rudin-Blass Ordering of Measures. https://arxiv.org/abs/2504.14678

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