The Vitali Integral Convergence Theorem and Uniform Absolute Continuity
Canadian journal of mathematics, Tome 43 (1991) no. 5, pp. 939-947

Voir la notice de l'article provenant de la source Cambridge University Press

A geometric version of the Vitali integral convergence theorem is established. Parameterized versions of results on uniform absolute continuity in spaces of measures suggested by the convergence theorem are studied.
DOI : 10.4153/CJM-1991-051-3
Mots-clés : 46B20, 46A50, 28A33, 28A99, Vitali integral convergence theorem, uniform absolute continuity, Gateaux differentiability
Bator, Elizabeth M.; Bilyeu, Russell G.; Lewis, Paul W. The Vitali Integral Convergence Theorem and Uniform Absolute Continuity. Canadian journal of mathematics, Tome 43 (1991) no. 5, pp. 939-947. doi: 10.4153/CJM-1991-051-3
@article{10_4153_CJM_1991_051_3,
     author = {Bator, Elizabeth M. and Bilyeu, Russell G. and Lewis, Paul W.},
     title = {The {Vitali} {Integral} {Convergence} {Theorem} and {Uniform} {Absolute} {Continuity}},
     journal = {Canadian journal of mathematics},
     pages = {939--947},
     year = {1991},
     volume = {43},
     number = {5},
     doi = {10.4153/CJM-1991-051-3},
     url = {http://geodesic.mathdoc.fr/articles/10.4153/CJM-1991-051-3/}
}
TY  - JOUR
AU  - Bator, Elizabeth M.
AU  - Bilyeu, Russell G.
AU  - Lewis, Paul W.
TI  - The Vitali Integral Convergence Theorem and Uniform Absolute Continuity
JO  - Canadian journal of mathematics
PY  - 1991
SP  - 939
EP  - 947
VL  - 43
IS  - 5
UR  - http://geodesic.mathdoc.fr/articles/10.4153/CJM-1991-051-3/
DO  - 10.4153/CJM-1991-051-3
ID  - 10_4153_CJM_1991_051_3
ER  - 
%0 Journal Article
%A Bator, Elizabeth M.
%A Bilyeu, Russell G.
%A Lewis, Paul W.
%T The Vitali Integral Convergence Theorem and Uniform Absolute Continuity
%J Canadian journal of mathematics
%D 1991
%P 939-947
%V 43
%N 5
%U http://geodesic.mathdoc.fr/articles/10.4153/CJM-1991-051-3/
%R 10.4153/CJM-1991-051-3
%F 10_4153_CJM_1991_051_3

[1] 1. Bartle, R.G., Dunford, N., and Schwartz, J.T., Weak compactness and vector measures, Canad. J. Math. 7 (1955), 289–305. Google Scholar

[2] 2. Bilyeu, R.G. and Lewis, P.W., Uniform differentiability, uniform absolute continuity, and the Vitali-Hahn- Saks theorem, Rocky Mtn. J. Math. 10 (1980), 533–557. Google Scholar

[3] 3. Brooks, J.K., Equicontinuous sets of measures and applications to Vitali's integral convergence theorem and control measures, Advances in Math. 10 (1973), 165–171. Google Scholar

[4] 4. Brooks, J.K. and Jewett, R.S., On finitely additive vector measures, Proc. Nat. Acad. Sci. U.S.A. 67 (1970), 1294–1298. Google Scholar

[5] 5. Diestel, J., Geometry of Banach spaces—selected topics. Lecture Notes in Math., 485, Springer-Verlag, New York, 1975. Google Scholar

[6] 6. Rockafellar, R.T., Local boundedness of nonlinear, monotone operators, Michigan Math. J. 16(1969), 397–407. Google Scholar

[7] 7. Rockafellar, R.T., On the maximal monotonicity of subdifferential mappings, Pacific J. Math. 33 (1970), 200–216. Google Scholar

[8] 8. Royden, H.L., Real analysis. The Macmillian Company, Toronto, Canada. Google Scholar

Cité par Sources :