Hostname: page-component-cd9895bd7-p9bg8 Total loading time: 0 Render date: 2024-12-25T01:20:09.740Z Has data issue: false hasContentIssue false
  • English
  • Français

Yet another short proof of the Riesz representation theorem

Published online by Cambridge University Press:  24 October 2008

David Ross
David Ross
Affiliation:
Department of Pure Mathematics, University of Hull, Hull HU6 7RX
Get access Rights & Permissions [Opens in a new window]

Extract

F. Riesz's ‘Representation Theorem’ has been proved by methods classical [11, 12], category-theoretic [7], and functional-analytic [2, 9]. (Garling's remarkable proofs [5, 6] owe their brevity to the combined strength of these and other methods.) These proofs often reveal a connection between the Riesz theorem and some unexpected area of mathematics.

Type
Research Article
Information
Mathematical Proceedings of the Cambridge Philosophical Society , Volume 105 , Issue 1 , January 1989 , pp. 139 - 140
Copyright
Copyright © Cambridge Philosophical Society 1989

Access options

Get access to the full version of this content by using one of the access options below. (Log in options will check for institutional or personal access. Content may require purchase if you do not have access.)

References

REFERENCES

[1]Cutland, N.. Nonstandard measure theory and its applications. Bull. London Math. Soc. 15 (1983), 529–589.CrossRefGoogle Scholar
[2]Dellacherie, C. and Meyer, P.-A.. Probabilities and Potential (North Holland, 1978).Google Scholar
[3]Farkas, J.. Über die Theorie der einfachen Ungleichungen, J. Math. 124 (1902), 1–24.Google Scholar
[4]Franklin, J.. Mathematical models of economics. Amer. Math. Monthly 90 (1983), 229–244.CrossRefGoogle Scholar
[5]Garling, D. J. H.. A ‘short’ proof of the Riesz representation theorem. Math. Proc. Cambridge Philos. Soc. 73 (1973), 459–460.CrossRefGoogle Scholar
[6]Garling, D. J. H.. Another ‘short’ proof of the Riesz representation theorem. Math. Proc. Cambridge Philos. Soc. 99 (1986), 261–262.CrossRefGoogle Scholar
[7]Hartig, D. G.. The Riesz representation revisited. Amer. Math. Monthly 90 (1983), 277–280.CrossRefGoogle Scholar
[8]Loeb, P. A.. An introduction to nonstandard analysis and hyperfinite measure theory. In Probabilistic Analysis and Related Topics, vol. 11 (Academic Press, 1979), pp. 105–142.CrossRefGoogle Scholar
[9]Loeb, P. A.. A functional approach to nonstandard measure theory. Contemp. Math. 26 (1984), 251–261.CrossRefGoogle Scholar
[10]Rockafeller, R. T.. Convex Analysis (Princeton University Press, 1970).CrossRefGoogle Scholar
[11]Rudin, W.. Real and Complex Analysis (McGraw-Hill. 1966).Google Scholar
[12]Zivaljevic, R.. A Loeb measure approach to the Riesz representation theorem. Publ. Inst. Math. (Beograd) (N.S.) 32 (1982), 175–177.Google Scholar