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Some examples of nonmeasurable sets

Published online by Cambridge University Press:  09 April 2009

Edwin Hewitt  and
Karl Stromberg
Edwin Hewitt
Affiliation:
The University of Washington, Seattle, U.S.A.
Karl Stromberg
Affiliation:
The University of Washington, Seattle, U.S.A.
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In a recent issue of this Journal, Pu [3] has given an interesting construction of a nonmeasurable subset A of R such that for all intervals I in R. [Throughout this note, the symbol λ denotes Lebesgue outer measure on R or Haar outer measure on a general locally compact group.] This solves a problem stated in [2], p. 295, Exercise (18.30).

Type
Research Article
Information
Journal of the Australian Mathematical Society , Volume 18 , Issue 2 , September 1974 , pp. 236 - 238
Copyright
Copyright © Australian Mathematical Society 1974

References

[1]Hewitt, Edwin, and Ross, Kenneth A., Abstract Harmonic Analysis, Vol. I (New York — Heidelberg — Berlin: Springer-Verlag 1963).Google Scholar
[2]Hewitt, Edwin, and Stromberg, Karl R., Real and Abstract Analysis, 2nd printing. (New York — Heidelberg — Berlin: Springer-Verlag 1969).Google Scholar
[3]Pu, H. W., ‘Concerning non-measurable subsets of a given measurable set’, J. Austral. Math. Soc. 13 (1972), 267–270.CrossRefGoogle Scholar
[4]Sierpiński, W., ‘Sur un problème conduisant à un ensemble non mesurable’. Fund. Math. 10 (1927), 177–179.CrossRefGoogle Scholar