Exhaustive submeasures on Boolean rings, Banach lattices and uniform absolute continuity

• Autorzy: Huff C. , Lewis P.
• Języki publikacji: EN

Abstrakty

EN

A bi-sequential version of a classical theorem dealing with uniform absolute continuity in spaces of measures is extended to the setting of submeasures on a Boolean ring. Applications to spaces of vector measures and Banach lattices are discussed.

Słowa kluczowe

EN

absolute continuity; Banach lattice; Boolean ring; exhaustivity; submeasure

PL

ciągłość absolutna; krata Banacha; pierścień Boole'a; submiara

• Wydawca: Instytut Matematyczny PAN
• Czasopismo: Bulletin of the Polish Academy of Sciences. Mathematics
• Rocznik: 2001
• Tom: Vol. 49, no 3
• Strony: 203--210
• Opis fizyczny: Bibliogr. 11 poz.

Twórcy

autor

Huff C.

• Department of Mathematics, Box 305118, University of North Texas, Denton, TX 76203-5118, USA.

autor

Lewis P.

• Department of Mathematics, Box 305118, University of North Texas, Denton, TX 76203-5118, USA.

Bibliografia

• [1] E. Bator, R. Bilyeu, P. Lewis, The Vitali integral convergence theorem and uniform absolute continuity, Canad. J. Math., 43 (1991) 939-947.
• [2] W. Bell, R. Bilyeu, P. Lewis, Uniform exhaustivity and Banach lattices, Ann. Mat. Pura Appl., CXLIV(1986) 57-74.
• [3] R. Bilyeu., P. Lewis, Uniform, differentiability, uniform absolute continuity, and the Vitali-Hahn-Saks theorem, Rocky Mountain J. Math., 10 (1980) 533-557.
• [4] J. Brooks, Equicontinuous sets of measures and applications to Vitali's integral convergence theorem and control measures, Adv. Math., 10 (1973) 165-171.
• [5] J. Diestel, J. J. Uhl, Jr., Vector measures, Math. Surveys Monogr., (15) (1977).
• [6] L. Drewnowski, Topological rings of sets, continuous set functions, integration, II, Bull. Acad. Pol. Sci., Sér. mat., 20 (4)(1972) 277-286.
• [7] L. Drewnowski, Decomposition of set functions, Studia Math., 48 (1973) 23-48.
• [8] L. Drewnowski, I. Labuda, Copies of co and t∞ in topological Riesz spaces, Trans. Amer. Math. Soc., 350 (1998) 3555-3570.
• [9] J. Lindenstrauss, L. Tzafriri, Classical Banach spaces. II, Springer, Berlin 1977.
• [10] W. A. J. Luxemburg, A. C. Zaanen, .Riesz Spaces, Vol. 1, North-Holland Publishing Company, Amsterdam 1971.
• [11] H. Schaefer, Banach Lattices and Positive Operators, Springer, New York 1974.