Basic Sequences in the Space of Measurable Functions

Casper Goffman, Daniel Waterman
1960 Proceedings of the American Mathematical Society  
1. In a topological vector space X, a basic sequence [xn] is one whose finite linear combinations are dense in X. In a recent work, [l], A. A. Talalyan has observed that the space of measurable functions has a distinctly different character, with respect to the behavior of basic sequences, from, for example, the Lp spaces, p^l. A striking result of Talalyan is the fact that if {"} is basic, i.e., for every measurable , there are finite linear combinations of the , then if any finite number of
more » ... finite number of functions is deleted from {"}, the remaining sequence is basic. This readily implies the existence of universal expansions, and the existence of a subsequence \2, i.
doi:10.2307/2032957 fatcat:c5fxqwo7gzeebnxghunndyywye