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A simple proof of Müntz's theorem

Published online by Cambridge University Press:  24 October 2008

L. C. G. Rogers
L. C. G. Rogers
Affiliation:
University of Warwick
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Extract

Let 0 < λ1 < λ2 < … be an increasing sequence of positive reals tending to infinity, and let ν1, ν2 be two (finite) signed measures on ℝ+ such that

for all k. It was originally proved by Müntz (12) that, if

then ν1 = ν2, and, conversely, if this condition fails, then there exist distinct ν1 and ν2 satisfying (1).

Type
Research Article
Information
Mathematical Proceedings of the Cambridge Philosophical Society , Volume 90 , Issue 1 , July 1981 , pp. 1 - 3
Copyright
Copyright © Cambridge Philosophical Society 1981

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References

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