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Uniformly exhaustive submeasures and nearly additive set functions. (English) Zbl 0524.28008

##### MSC:
 28A60 Measures on Boolean rings, measure algebras 28A12 Contents, measures, outer measures, capacities 46A04 Locally convex Fréchet spaces and (DF)-spaces 28B05 Vector-valued set functions, measures and integrals
##### Keywords:
uniformly exhaustive submeasure; control measure
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##### References:
 [1] Jens Peter Reus Christensen, Some results with relation to the control measure problem, Vector space measures and applications (Proc. Conf., Univ. Dublin, Dublin, 1977) Lecture Notes in Math., vol. 645, Springer, Berlin-New York, 1978, pp. 27 – 34. [2] Wojchiech Herer and Jens Peter Reus Christensen, On the existence of pathological submeasures and the construction of exotic topological groups, Math. Ann. 213 (1975), 203 – 210. · Zbl 0311.28002 [3] Lech Drewnowski, Un théorème sur les opérateurs de \?_{\infty }(\Gamma ), C. R. Acad. Sci. Paris Sér. A-B 281 (1975), no. 22, Aii, A967 – A969 (French, with English summary). · Zbl 0323.46014 [4] Ofer Gabber and Zvi Galil, Explicit constructions of linear-sized superconcentrators, J. Comput. System Sci. 22 (1981), no. 3, 407 – 420. Special issued dedicated to Michael Machtey. · Zbl 0487.05045 [5] P. Hall, On representatives of subsets, J. London Math. Soc. 10 (1935), 26-30. · Zbl 0010.34503 [6] N. J. Kalton, Linear operators whose domain is locally convex, Proc. Edinburgh Math. Soc. (2) 20 (1976/77), no. 4, 293 – 299. · Zbl 0392.46012 [7] N. J. Kalton, The three space problem for locally bounded \?-spaces, Compositio Math. 37 (1978), no. 3, 243 – 276. · Zbl 0395.46003 [8] Gerald A. Goldin and Robert F. Wheeler , Measure theory and its applications, Northern Illinois University, Department of Mathematical Sciences, DeKalb, Ill., 1981. · Zbl 0451.00005 [9] -, Isomorphisms between spaces of vector-valued continuous functions, Proc. Edinburgh Math. Soc. (to appear). · Zbl 0527.46026 [10] J. L. Kelley, Measures on Boolean algebras, Pacific J. Math. 9 (1959), 1165 – 1177. · Zbl 0087.04801 [11] Dorothy Maharam, An algebraic characterization of measure algebras, Ann. of Math. (2) 48 (1947), 154 – 167. · Zbl 0029.20401 [12] M. S. Pinsker, On the complexity of a concentrator, 318/1-318/4, 7th Internat. Telegraphic Conf., Stockholm, June 1973. [13] Nicholas Pippenger, Superconcentrators, SIAM J. Comput. 6 (1977), no. 2, 298 – 304. · Zbl 0361.05035 [14] V. A. Popov, Additive and semiadditive functions on Boolean algebras, Sibirsk. Mat. Ž. 17 (1976), no. 2, 331 – 339, 479 (Russian). · Zbl 0354.28013 [15] M. Ribe, Examples for the nonlocally convex three space problem, Proc. Amer. Math. Soc. 73 (1979), no. 3, 351 – 355. · Zbl 0397.46002 [16] J. W. Roberts, Pathological compact convex sets in the spaces $${L_p},0 < p < 1$$, The Altgeld Book, University of Illinois, 1976. [17] James W. Roberts, A compact convex set with no extreme points, Studia Math. 60 (1977), no. 3, 255 – 266. · Zbl 0397.46010 [18] -, A non-locally convex $$F$$-space with the Hahn-Banach approximation property, Banach Spaces of Analytic Functions, Lecture Notes in Math., vol. 604, Springer-Verlag, Berlin and New York, 1977, pp. 76-82. [19] S. Rolewicz and C. Ryll-Nardzewski, On unconditional convergence in linear metric spaces, Colloq. Math. 17 (1967), 327 – 331. · Zbl 0166.10401 [20] M. Simonard, Linear programming, Prentice-Hall, Englewood Cliffs, N. J., 1967. [21] Michel Talagrand, A simple example of pathological submeasure, Math. Ann. 252 (1979/80), no. 2, 97 – 102. · Zbl 0444.28003
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