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Search: All articles in the CMB digital archive with keyword function space

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1. CMB 2008 (vol 51 pp. 570)

Lutzer, D. J.; Mill, J. van; Tkachuk, V. V.
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)

Kikuchi, Masato
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

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