1. CMB 2008 (vol 51 pp. 570)
|Amsterdam Properties of $C_p(X)$ Imply Discreteness of $X$ |
We prove, among other things, that if $C_p(X)$ is subcompact in the sense of de Groot, then the space $X$ is discrete. This generalizes a series of previous results on completeness properties of function spaces.
Keywords:regular filterbase, subcompact space, function space, discrete space
Categories:54B10, 54C05, 54D30
2. CMB 1999 (vol 42 pp. 321)
|Averaging Operators and Martingale Inequalities in Rearrangement Invariant Function Spaces |
We shall study some connection between averaging operators and martingale inequalities in rearrangement invariant function spaces. In Section~2 the equivalence between Shimogaki's theorem and some martingale inequalities will be established, and in Section~3 the equivalence between Boyd's theorem and martingale inequalities with change of probability measure will be established.
Keywords:martingale inequalities, rearrangement invariant function spaces
Categories:60G44, 60G46, 46E30