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Abstrakty
Exhaustive and uniformly exhaustive elements are studied in the setting of locally solid topological Riesz spaces with the principal projection property. We study the structure of the order interval [O, χ] when x is an exhaustive element and the structure of the solid hull of a set of uniformly exhaustive elements.
Wydawca
Rocznik
Tom
Strony
53--62
Opis fizyczny
Bibliogr. 19 poz.
Twórcy
autor
- Department of Mathematics, Lake Superior State University, Sault Sainte Marie, MI 49783, U.S.A., kmuller@lssu.edu
Bibliografia
- [1] C. Aliprantis and O. Burkinshaw, Locally Solid Riesz Spaces, Academic Press, New York, 1978.
- [2] —, —, Positive Operators, Academic Press, New York, 1985.
- [3] W. Bell, R. Bilyeu and P. Lewis, Uniform exhaustivity and Banach lattices, Ann. Mat. Pura Appl. 4 (1944), 57-74.
- [4] R. Bilyeu and P. Lewis, Uniform differentiability, uniform absolute continuity, and the Vitali-Hahn Saks theorem, Rocky Mountain J. Math. 10 (1980), 533-557.
- [5] J. Brooks, Equicontinuous sets of measures and applications to Vitali 's integral convergence theorem and control measures, Ad. Math. 10 (1973), 165-171.
- [6] J. Brooks and R. Jewett, On finitely additive vector measures, Proc. Nat. Acad. Sci. U.S.A. 67 (1970), 1294-1298.
- [7] J. Brooks and P. Lewis, Linear operators and vector measures, Trans. Amer. Math. Soc. 192 (1974), 139-162.
- [8] J. Diestel and B. Faires, On vector measures, ibid. 198 (1974), 253-271.
- [9] J. Diestel and J. Uhl, Vector Measures, Math. Surveys 15, Amer. Math. Soc., Providence, 1977.
- [10] L. Drewnowski, Equivalence of Brooks-Jewett, Vitali-Hahn-Saks and Nikodym theorems, Bull. Acad. Polon. Sci. Ser. Sci. Math. Astronom. Phys. 20 (1972), 725-731.
- [11] —, Topological rings of sets, continuous set functions, integration. II, ibid. 80 (1972), 277-286.
- [12] L. Drewnowski and I. Labuda, Copies of Co and l∞ in topological Riesz spaces, Trans. Amer. Math. Soc. 350 (1998), 3555-3570.
- [13] C. Huff and P. Lewis, Exhaustive submeasures on boolean rings, Banach lattices, and uniform absolute continuity. Bull. Polish Acad. Sci. Math. 49 (2001), 203-210.
- [14] S. Kakutani, Concrete representation of abstract (L)-spaces, Ann. of Math. 42 (1941), 523-537.
- [15] —, Notes on infinite product measure spaces II, Proc. Imp. Acad. Tokyo 19 (1943), 184-188.
- [16] P. Lewis and K. Muller, Isomorphic embeddings and strongly additive measures, Monatsh. Math. 143 (2004), 21-33.
- [17] W. Luxemburg and A. Zaanen, Riesz Spaces, Vol. 1, North-Holland, Amsterdam, 1971.
- [18] P. Meyer-Nieberg, Zur schwachen Kompaktheit in Banachverbänden, Math. Z. 134 (1973), 303-315.
- [19] H. Schaefer, Banach Lattices and Positive Operators, Springer, New York, 1974.
Typ dokumentu
Bibliografia
Identyfikator YADDA
bwmeta1.element.baztech-article-BAT5-0011-0014