Hostname: page-component-78c5997874-94fs2 Total loading time: 0 Render date: 2024-11-15T06:05:40.739Z Has data issue: false hasContentIssue false
  • English
  • Français

On the role of L-Baire functions in abstract measure and integration

Published online by Cambridge University Press:  18 May 2009

Melvin J. Maron
Melvin J. Maron
Affiliation:
University of Louisville
Rights & Permissions [Opens in a new window]

Extract

Core share and HTML view are not available for this content. However, as you have access to this content, a full PDF is available via the ‘Save PDF’ action button.

If X is any set and L ⊂ [ – ∞, ∞]x, the class ℬL of L-Baire functions is defined to be the smallest subclass of [ – ∞, ∞]x which contains L and is closed under the formation of monotone, pointwise, sequential limits, so that ℬL ∍ fn ↗ f or ℬL ∍ fn ↘ f ⇒ f ∊ ℬL.

Type
Research Article
Information
Glasgow Mathematical Journal , Volume 16 , Issue 1 , March 1975 , pp. 61 - 67
Copyright
Copyright © Glasgow Mathematical Journal Trust 1975

References

REFERENCES

1.Bogdanowicz, W. M., An approach to the theory of integration generated by positive line functionals and existence of minimal extensions. Proc. Japan Acad. 43 (1967) 186–191.Google Scholar
2.Halmos, P. R., Measure Theory (Van Nostrand Company, New Jersey, 1950).CrossRefGoogle Scholar
3.Kelly, J. L. and Srinnivasan, T. P. (Lecture Notes, University of Berkeley).Google Scholar
4.Loomis, L. H., An Introduction to Abstract Harmonic Analysis (Van Nostrand Company, New Jersey, 1953).Google Scholar
5.Maron, M. J., Abstract integral spaces and minimal extensions, Glasgow Math. J. 12 (1971), 166–178.CrossRefGoogle Scholar
6.Royden, H. L., Real Analysis, Second Edition (Macmillan Company, New York, 1968).Google Scholar
7.Segal, I. E. and Kunze, R. A., Integrals and Operators (McGraw-Hill Book Company, New York, 1968).Google Scholar
8.Stone, M. H., Notes on Integration. Proc. Nat. Acad. Set. U.S.A. 34 (1948), (I) 336–342, (II) 447–455, (III) 483–490,35 (1949), (IV) 50–58.CrossRefGoogle ScholarPubMed
9.Zaanen, A. C., Integration, Second Edition (North-Holland Publishing Company, Amsterdam, 1967).Google Scholar