Barycenters, pinnacle points, and denting points
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- by Surjit Singh Khurana PDF
- Trans. Amer. Math. Soc. 180 (1973), 497-503 Request permission
Abstract:
Some properties of probability measures, on closed convex bounded sets in locally convex spaces, having barycenters are obtained. Also some geometric and measure-theoretic characterizations of pinnacle points are given, and a result about denting points is proved.References
- Heinz Bauer and H. S. Bear, The part metric in convex sets, Pacific J. Math. 30 (1969), 15–33. MR 275101, DOI 10.2140/pjm.1969.30.15
- Richard D. Bourgin, Barycenters of measures on certain noncompact convex sets, Trans. Amer. Math. Soc. 154 (1971), 323–340. MR 271701, DOI 10.1090/S0002-9947-1971-0271701-X G. Choquet, Lectures on analysis. Vols. I, II, III, Benjamin, New York, 1969. MR 40 #3252; #3253; #3254.
- 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
- John L. Kelley, General topology, D. Van Nostrand Co., Inc., Toronto-New York-London, 1955. MR 0070144
- Surjit Singh Khurana, Measures and barycenters of measures on convex sets in locally convex spaces. I, J. Math. Anal. Appl. 27 (1969), 103–115. MR 243309, DOI 10.1016/0022-247X(69)90068-7
- Surjit Singh Khurana, Characterization of extreme points, J. London Math. Soc. (2) 5 (1972), 102–104. MR 312199, DOI 10.1112/jlms/s2-5.1.102
- Surjit Singh Khurana, Barycenters, extreme points, and strongly extreme points, Math. Ann. 198 (1972), 81–84. MR 331012, DOI 10.1007/BF01420499
- J. D. Knowles, Measures on topological spaces, Proc. London Math. Soc. (3) 17 (1967), 139–156. MR 204602, DOI 10.1112/plms/s3-17.1.139
- Robert R. Phelps, Lectures on Choquet’s theorem, D. Van Nostrand Co., Inc., Princeton, N.J.-Toronto, Ont.-London, 1966. MR 0193470
- J. D. Pryce, On the representation and some separation properties of semi-extremal subsets of convex sets, Quart. J. Math. Oxford Ser. (2) 20 (1969), 367–382. MR 251492, DOI 10.1093/qmath/20.1.367
- M. A. Rieffel, Dentable subsets of Banach spaces, with application to a Radon-Nikodým theorem, Functional Analysis (Proc. Conf., Irvine, Calif., 1966) Academic Press, London; Thompson Book Co., Washington, D.C., 1967, pp. 71–77. MR 0222618
- Helmut H. Schaefer, Topological vector spaces, The Macmillan Company, New York; Collier Macmillan Ltd., London, 1966. MR 0193469
- Dieter Sondermann, Masse auf lokalbeschränkten Räumen, Ann. Inst. Fourier (Grenoble) 19 (1969), no. fasc. 2, 33–113 (1970) (German, with English and French summaries). MR 260967, DOI 10.5802/aif.322 F. Topsøe, Measure and topology, Lecture Notes in Math., vol. 133, Springer-Verlag, New York, 1970.
- V. S. Varadarajan, Measures on topological spaces, Mat. Sb. (N.S.) 55 (97) (1961), 35–100 (Russian). MR 0148838
Additional Information
- © Copyright 1973 American Mathematical Society
- Journal: Trans. Amer. Math. Soc. 180 (1973), 497-503
- MSC: Primary 28A40; Secondary 46A05
- DOI: https://doi.org/10.1090/S0002-9947-1973-0318438-8
- MathSciNet review: 0318438