Illinois Journal of Mathematics

Residual measures

Thomas E. Armstrong and Karel Prikry

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simultaneous generalization of the normal Radon measures of Dixmier and the category measures of Oxtoby. We examine the regularity, $\tau$-smoothness, tightness, and support properties of residual measures. We show that residual measures without support exist iff real-valued measurable cardinals exist. In the compact setting we associate with any compact Hausdorff space $X$ a larger Stonian compact Hausdorf space, the Gleason space of $X$, such that there is a bijective correspondence between the residual measures on these spaces and the residual Radon measures on these spaces. Hence, we lift the question of existence of certain types of residual measures to the Stonian setting of Dixmier.

Article information

Illinois J. Math., Volume 22, Issue 1 (1978), 64-78.

First available in Project Euclid: 20 October 2009

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Zentralblatt MATH identifier

Primary: 28A32


Armstrong, Thomas E.; Prikry, Karel. Residual measures. Illinois J. Math. 22 (1978), no. 1, 64--78. doi:10.1215/ijm/1256048835.

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