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Basic Sequences in the Space of Measurable Functions

1960
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Proceedings of the American Mathematical Society
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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

doi:10.2307/2032957
fatcat:c5fxqwo7gzeebnxghunndyywye