| Title:
|
On integration in Banach spaces, VI (English) |
| Author:
|
Dobrakov, Ivan |
| Author:
|
Morales, Pedro |
| Language:
|
English |
| Journal:
|
Czechoslovak Mathematical Journal |
| ISSN:
|
0011-4642 (print) |
| ISSN:
|
1572-9141 (online) |
| Volume:
|
35 |
| Issue:
|
2 |
| Year:
|
1985 |
| Pages:
|
173-187 |
| Summary lang:
|
Russian |
| . |
| Category:
|
math |
| . |
| MSC:
|
28B05 |
| MSC:
|
46G10 |
| idZBL:
|
Zbl 0628.28007 |
| idMR:
|
MR787123 |
| DOI:
|
10.21136/CMJ.1985.102009 |
| . |
| Date available:
|
2008-06-09T15:04:25Z |
| Last updated:
|
2020-07-28 |
| Stable URL:
|
http://hdl.handle.net/10338.dmlcz/102009 |
| . |
| Reference:
|
[1] Bartle R.: A general bilinear integral.Studia Math. 15 (1956), 337-352. MR 0080721, 10.4064/sm-15-3-337-352 |
| Reference:
|
[2J Birkhoff G.: Integration of functions with values in a Banach space.Trans. Amer. Math. Soc. 38 (1935), 357-378. MR 1501815, 10.4064/fm-20-1-262-176 |
| Reference:
|
[3] Bochner S.: Integration von Funktionen deren Werte die Element eines Vectorraumes sind.Fund. Math. 20 (1933), 262-276. 10.1007/BF01954539 |
| Reference:
|
[4] Bryant W. W.: Independent axioms for convexity.J. Geometry 5 (1974), 95-99. Zbl 0288.52001, MR 0355820 |
| Reference:
|
[5] Bryant W. W.: Topological convexity spaces.Proc. Edinburgh Math. Soc. 19 (1974), 125-132. Zbl 0292.46007, MR 0417749, 10.1016/0022-247X(72)90268-5 |
| Reference:
|
[6] Bryant W. W., Webster R. J.: Convexity spaces I.J. Math. Anal. Appl. 37 (1972), 206-213. Zbl 0197.48401, MR 0296812, 10.1016/0022-247X(73)90076-0 |
| Reference:
|
[7] Bryant W. W., Webster R. J.: Convexity spaces II.J. Math. Anal. Appl. 43 (1973), 321-327. Zbl 0259.52001, MR 0380622, 10.1016/0022-247X(77)90267-0 |
| Reference:
|
[8] Bryant W. W., Webster R. J.: Convexity spaces III.J. Math. Anal. Appl. 57 (1977), 382 to 392. Zbl 0342.52001, MR 0467541, 10.1090/pspum/007/0157289 |
| Reference:
|
[9] Danzer L., Grünbaum В., Klee V.: Helly's theorems and its relatives.Proc. Sympos. Pure Math. Vol. VII(convexity). Amer. Math. Soc. (1963), 101-180. |
| Reference:
|
[10] Diestel J., Uhl J. J.: Vector measures.Math. Surveys 15, Amer. Math. Soc., Providence, Rhode Island 1977. Zbl 0369.46039, MR 0453964 |
| Reference:
|
[11] Dieudonné J.: Foundations of Modern Analysis.Academic Press, New York 1960. MR 0120319 |
| Reference:
|
[12] Dinculeanu N.: Vector measures.Pergamon Press, New York 1967. MR 0206190 |
| Reference:
|
[13] Dobrakov I.: On integration in Banach spaces I.Czechoslovak Math. J. 20 (1970), 511- 536. Zbl 0215.20103, MR 0365138 |
| Reference:
|
[14] Dobrakov I.: On integration in Banach spaces II.Czechoslovak Math. J. 20 (1970), 680- 695. Zbl 0224.46050, MR 0365139 |
| Reference:
|
[15] Dobrakov I.: On integration in Banach spaces III.Czechoslovak Math. J. 29 (1979), 478-499. Zbl 0429.28011, MR 0536071 |
| Reference:
|
[16] Dobrakov I.: Оn integration, in Banach spaces IV.Czechoslovak Math. J. 30 (1980), 259-279. MR 0566051 |
| Reference:
|
[17] Dobrakov I.: On integration in Banach spaces V.Czechoslovak Math. J. 30 (1980), 610- 622. Zbl 0506.28004, MR 0592324, 10.1090/S0002-9947-1935-1501796-2 |
| Reference:
|
[18] Dunford N.: Integration in general analysis.Trans. Amer. Math. Soc. 37 (1935), 441 - 453. Zbl 0013.15502, MR 1501796 |
| Reference:
|
[19] Dunford N., Schwartz J. T.: Linear operators. Part I.Interscience Publishers, Inс., New York 1964. 10.1007/BF01302165 |
| Reference:
|
[20] Eckhoff J.: Der Satz von Radon in konvexen Produktstructuren I.Monatsh. Math. 72 (1968), 303-314. MR 0233285, 10.1007/BF01297698 |
| Reference:
|
[21] Eckhoff J.: Der Satz von Radon in konvexen Produktstructuren II.Monatsh. Math. 73 (1969), 7-30. MR 0243427, 10.1215/S0012-7094-52-01941-8 |
| Reference:
|
[22] Ellis J. W.: A general set-separation theorem.Duke Math. J. 19 (1952), All-All. Zbl 0047.28601, MR 0049268, 10.4153/CJM-1950-046-x |
| Reference:
|
[23] Green J. W., Gustin W.: Quasiconvex sets.Canad. J. Math. 2 (1950), 489-507. Zbl 0038.35501, MR 0042142 |
| Reference:
|
[24] Guay M. D., Naimpally S. A.: Characterization of a convex subspace of a linear topological space.Math. Japonicae 20 (1975), 37-41. Zbl 0335.46008, MR 0410334 |
| Reference:
|
[25] Hanner O.: Connectedness and convex hulls.Seminar on Convex Sets, Inst. for Advanced Study, Princeton, New Jersey (1949-1950), 35-40. 10.1090/S0002-9947-1934-1501772-9 |
| Reference:
|
[26] Hildebrandt T. H.: On bounded linear functional operations.Trans. Amer. Math. Soc. 36 (1934), 868-875. Zbl 0010.30303, MR 1501772, 10.2140/pjm.1971.38.471 |
| Reference:
|
[27] Kay D. C, Womble E. W.: Axiomatic convexity theory and relationships between the Carathéorody, Helly and Radon numbers.Pacific J. Math. 38 (1971), 471 - 485. MR 0310766 |
| Reference:
|
[28] Kelley J. L., Srinivasan T. P.: On the Bochner integral.Proc. Conf. Vector and Operator-valued Measures, Snowbird, Utah, Academic Press (1973), 165-174. Zbl 0293.28010, MR 0330408, 10.1007/BF01455714 |
| Reference:
|
[29] Kolmogoroff A.: Untersuchunge über den Integralbegriff.Math. Ann. 103 (1930), 654-696. |
| Reference:
|
[30] Levi F. W.: On Helly's theorem and the axioms of convexity.J. Indian Math. Soc. (N.S.) 15(1951), 65-76. Zbl 0044.19101, MR 0043487, 10.1112/jlms/s2-13.2.209 |
| Reference:
|
[31] Mah P., Naimpally S. A., Whitfield J. H. M.: Linearization of a convexity space.J. London Math. Soc. (2) 13 (1976), 209-214. Zbl 0326.52005, MR 0415510 |
| Reference:
|
[32] Maynard H. В.: A general Radon-Nikodym theorem.Proc. Conf. Vector and Operator-valued Measures, Snowbird, Utah, Academic Press (1973), 233 - 246. Zbl 0301.28006, MR 0404578 |
| Reference:
|
[33] McLeod R.: Mean value theorem for vector valued functions.Proc. Edinburgh Math. Soc. 14(1965), 197-209. MR 0185052 |
| Reference:
|
[34] Morales P.: Mean value theorem for the Dobrakov integral.Proc. Conf. on Measure Theory and Appl., Northern Illinois University (1981), 235-242. Zbl 0523.28009 |
| Reference:
|
[35] Prenowitz W.: A contemporary approach to classical geometry.H.E. Slaught Memorial Paper 9, Amer. Math. Monthly 68 (1961), Appendix, 1--67. Zbl 0094.15402, MR 0123931 |
| Reference:
|
[36] Prenowitz W., Jantosciak J.: Geometries and join spaces.J. Reine Angew. Math. 257 (1972), 100-128. Zbl 0264.50002, MR 0308908, 10.1090/S0002-9947-1940-0001442-5 |
| Reference:
|
[37] Price G. В.: The theory of integration.Trans. Amer. Math. Soc. 47 (1940), 1 - 50. Zbl 0022.31901, MR 0001442, 10.2140/pjm.1970.35.227 |
| Reference:
|
[38] Reay J. R.: Carathéodory theorems in convex product structures.Pacific J. Math. 35 (1970), 227-230. Zbl 0182.55601, MR 0273517, 10.5802/aif.17 |
| Reference:
|
[39] Schwartz L.: Un lemme sur la dérivation des fonctions vectorielles d'une variable réelle.Ann. Inst. Fourier 2 (1950), 17-18. Zbl 0042.11601, MR 0042610, 10.1007/BF02787718 |
| Reference:
|
[40] Schwartz L.: Espaces de fonctions différentiables à valeurs vectorielles.J. Analyse Math. 4 (1956), 88-148. MR 0080268 |
| Reference:
|
[41] Schwartz L.: Analyse mathématique I.Hermann, Paris 1967. MR 0226972, 10.4153/CMB-1976-073-0 |
| Reference:
|
[42] Szafron S. A., Weston J. H.: An internal solution to the problem of linearization of a convexity space.Canad. Math. Bull. 19 (1976), 487-494. Zbl 0382.52002, MR 0450940 |
| Reference:
|
[43] Taylor A. E.: Introduction to functional analysis.John Wiley and Sons, Inc., New York 1958. Zbl 0081.10202, MR 0098966 |
| Reference:
|
[44] Yamamuro S.: Differential calculus in topological linear spaces.Lecture Notes in Math. 374, Springer-Verlag, New York 1974. Zbl 0276.58001, MR 0488118 |
| . |
