## Illinois Journal of Mathematics

### Residual measures

#### Abstract

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

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

Dates
First available in Project Euclid: 20 October 2009

https://projecteuclid.org/euclid.ijm/1256048835

Digital Object Identifier
doi:10.1215/ijm/1256048835

Mathematical Reviews number (MathSciNet)
MR0460581

Zentralblatt MATH identifier
0369.28005

Subjects
Primary: 28A32

#### Citation

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