Includes material for a standard graduate class, advanced material not covered by the
standard course but necessary in order to read research literature in the area, and extensive …

Given a compact space K, we denote by P (K) the space of all Radon probability measures
on K, equipped with the weak* topology inherited from C (K)*. For nonmetrizable compacta …

Integration on topological spaces is a field of mathematics which could be defined as the
intersection of functional analysis, general topology, and probability theory. However, at …

We present a connected version of the compact L-space constructed by Kenneth Kunen
under CH. We show that this provides a Corson compact space K such that the Banach …

We prove that if $ K $ is a compact space and the space $ P (K\times K) $ of regular
probability measures on $ K\times K $ has countable tightness in its $ weak^* $ topology …

We construct a compact Hausdorff space KK such that the space P (K) P(K) of Radon
probability measures on KK considered with the weak∗ weak^* topology (induced from the …

Abstract top We investigate the problem if every compact space K carrying a Radon
measure of Maharam type κ can be continuously mapped onto the Tikhonov cube [0, 1] κ (κ …

Assuming that a compact space K carries a Radon measure of an uncountable Maharam
type K, we investigate if the space P (K)(of probability measures on K) or the space K itself …

The assertion every Radon measure defined on a first-countable compact space is uniformly
regular is shown to be relatively consistent. We prove an analogous result on the existence …

We consider Radon measures μ and pairs (κ, λ) of cardinals such that among every κ many
positive measure sets there are λ many whose intersection is nonempty. Such families are …