uniform boundedness principle

(redirected from Uniform boundedness theorem)

uniform boundedness principle

[′yü·nə‚fȯrm ′bau̇n·dəd·nəs ‚prin·sə·pəl]
(mathematics)
A family of pointwise bounded, real-valued continuous functions on a complete metric space X is uniformly bounded on some open subset of X.
McGraw-Hill Dictionary of Scientific & Technical Terms, 6E, Copyright © 2003 by The McGraw-Hill Companies, Inc.
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By (35) and Uniform Boundedness Theorem, we obtain N := [sup.sub.s[greater than or equal to]0] [parallel] [S.sub.s] [parallel] < [infinity].
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