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.