Regularity of Baire measures
Authors:
N. Dinculeanu and Paul W. Lewis
Journal:
Proc. Amer. Math. Soc. 26 (1970), 92-94
MSC:
Primary 28.50
DOI:
https://doi.org/10.1090/S0002-9939-1970-0260968-4
MathSciNet review:
0260968
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Abstract | References | Similar Articles | Additional Information
Abstract: In a recent paper N. Dinculeanu and I. Kluvánek showed that any Baire measure with values in a locally convex topological vector space is regular. Their construction depended heavily on the regularity of nonnegative Baire measures. In the present paper, a proof of the regularity is given which holds at once for the nonnegative case and the vector case.
- N. Dinculeanu and I. Kluvanek, On vector measures, Proc. London Math. Soc. (3) 17 (1967), 505–512. MR 214722, DOI https://doi.org/10.1112/plms/s3-17.3.505
- Nelson Dunford and Jacob T. Schwartz, Linear Operators. I. General Theory, Pure and Applied Mathematics, Vol. 7, Interscience Publishers, Inc., New York; Interscience Publishers, Ltd., London, 1958. With the assistance of W. G. Bade and R. G. Bartle. MR 0117523
- G. G. Gould, Integration over vector-valued measures, Proc. London Math. Soc. (3) 15 (1965), 193–225. MR 174694, DOI https://doi.org/10.1112/plms/s3-15.1.193
- Paul R. Halmos, Measure Theory, D. Van Nostrand Company, Inc., New York, N. Y., 1950. MR 0033869
- P. W. Lewis, Some regularity conditions on vector measures with finite semi-variation, Rev. Roumaine Math. Pures Appl. 15 (1970), 375–384. MR 264027
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Additional Information
Keywords:
Baire <IMG WIDTH="18" HEIGHT="20" ALIGN="BOTTOM" BORDER="0" SRC="images/img1.gif" ALT="$\sigma$">-ring,
regular Baire measures,
<IMG WIDTH="16" HEIGHT="37" ALIGN="MIDDLE" BORDER="0" SRC="images/img2.gif" ALT="$p$">-quasi-variation,
monotone ring of sets
Article copyright:
© Copyright 1970
American Mathematical Society