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A ‘short’ proof of the Riesz representation theorem

Published online by Cambridge University Press:  24 October 2008

D. J. H. Garling
D. J. H. Garling
Affiliation:
St John's College, Cambridge
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Extract

Textbook proofs of the Riesz theorem on the representation of linear functionals on C(X) by measures tend to be self-contained, but consequently are rather long, and use ad hoc methods (see, for example (2, 4, 5)). The purpose of this note is to give a short proof by appealing to standard methods of modern analysis.

Type
Research Article
Information
Mathematical Proceedings of the Cambridge Philosophical Society , Volume 73 , Issue 3 , May 1973 , pp. 459 - 460
Copyright
Copyright © Cambridge Philosophical Society 1973

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References

REFERENCES

(1)Báez-Duate, L.C(X)* and Kolmogorov's consistency theorem for Cantor spaces. Studies in Appl. Math. 49 (1970), 401–403.CrossRefGoogle Scholar
(2)Dunford, N. and Schwartz, J. T.Linear operators, Part 1 (Interscience, New York, 1958).Google Scholar
(3)Gillman, L. and Jerison, M.Rings of continuous functions (Van Nostrand, New York, 1960).CrossRefGoogle Scholar
(4)Halmos, P. R.Measure Theory (Van Nostrand, New York, 1950).CrossRefGoogle Scholar
(5)Kingman, J. F. C. and Taylor, S. J.Introduction to measure and probability (Cambridge University Press, 1966).CrossRefGoogle Scholar
(6)Varadarajan, V. S.On a theorem of F.Riesz concerning the form of linear functionals. Fund. Math. 46 (1958), 209–220.CrossRefGoogle Scholar