A functional analysis proof of the existence of Haar measure on locally compact abelian groups

A functional analysis proof of the existence of Haar measure on locally compact abelian groups
HTML articles powered by AMS MathViewer

by Alexander J. Izzo PDF

Proc. Amer. Math. Soc. 115 (1992), 581-583 Request permission

A simple proof of the existence of Haar measure on locally compact abelian groups is given. The proof uses the Markov-Kakutani fixed-point theorem.

References

John B. Conway, A course in functional analysis, Graduate Texts in Mathematics, vol. 96, Springer-Verlag, New York, 1985. MR 768926, DOI 10.1007/978-1-4757-3828-5

Linear operators, Part

Leopoldo Nachbin, The Haar integral, D. Van Nostrand Co., Inc., Princeton, N.J.-Toronto-London, 1965. MR 0175995

Zum Haarschen mass in topologischen gruppen

1

Jean-Paul Pier, Amenable locally compact groups, Pure and Applied Mathematics (New York), John Wiley & Sons, Inc., New York, 1984. A Wiley-Interscience Publication. MR 767264
Walter Rudin, Fourier analysis on groups, Interscience Tracts in Pure and Applied Mathematics, No. 12, Interscience Publishers (a division of John Wiley & Sons, Inc.), New York-London, 1962. MR 0152834
Walter Rudin, Functional analysis, McGraw-Hill Series in Higher Mathematics, McGraw-Hill Book Co., New York-Düsseldorf-Johannesburg, 1973. MR 0365062