International Journal of Mathematics and Mathematical Sciences
Volume 6 (1983), Issue 3, Pages 431-447

On the lattice theory of function semi-norms

I. E. Schochetman and S. K. Tsui

Department of Mathematical Sciences, Oakland University, Rochester 48063, Michigan, USA

Received 11 October 1982

Copyright © 1983 I. E. Schochetman and S. K. Tsui. This is an open access article distributed under the Creative Commons Attribution License, which permits unrestricted use, distribution, and reproduction in any medium, provided the original work is properly cited.


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 setting.