On the lattice theory of function semi-norms

On the lattice theory of function semi-norms

We consider the lattice of function semi-norms over a measure space, as well as certain distinguished subsets. We determine which subsets are sublattices and, in turn, which of these are Dedekind complete. We also investigate the extent to which the distributive and DeMorgan Laws are valid in this s...

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Bibliographic Details
Main Authors: I. E. Schochetman, S. K. Tsui
Format: Article
Language:English
Published: Hindawi Limited 1983-01-01
Series:International Journal of Mathematics and Mathematical Sciences
Subjects:
function semi-norm
associate semi-norm
infimum
supremum
Riesz-Fisher property
strong and weak Fatou properties
infinite triangle inequality
absolutely continuous norm
(sub-) lattice
Dedekind completeness
distributive laws
DeMorgan's laws.
Online Access:http://dx.doi.org/10.1155/S0161171283000381

Internet

http://dx.doi.org/10.1155/S0161171283000381

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