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Remarks on the integrability in Banach spaces. (English) Zbl 0635.28005
The main aim of this note is to give a correct proof of Theorem 1 in the paper by Ch. Swartz [Math. Slovaca 33, 141-144 (1983; Zbl 0518.28004)].

MSC:
28B05 Vector-valued set functions, measures and integrals
46G10 Vector-valued measures and integration
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References:
[1] BESSAGA C., PELCZYŃSKI A.: On bases and unconditional convergence of series in Banach spaces. Studia Math. 17, 1958, 151-164. · Zbl 0084.09805 · eudml:216910
[2] DAY M. M.: Normed-Linear Spaces. Springer-Verlag, Berlin-Göttingen-Heidelberg, 1958. · Zbl 0082.10603
[3] DOBRAKOV I.: On integration in Banach spaces, I. Czech. Math. J. 20 (95), 1970, 51, 1-536. · Zbl 0215.20103 · eudml:12548
[4] DOBRAKOV I.: On integration in Banach spaces, II. Czech. Math. J. 20 (95), 1970, 680-695. · Zbl 0224.46050 · eudml:12558
[5] DOBRAKOV I.: On representation of linear operators on C(T, X). Czech. Math. J. 21 (96), 1971, 13-30. · Zbl 0225.47018 · eudml:12566
[6] DOBRAKOV I., FARKOVÁ J.: On submeasures II. Math. Slovaca 30, 1980, 65-81. · Zbl 0428.28001 · eudml:31571
[7] DUNFORD N., SCHWARTZ J.: Linear Operators. Part I, Interscience Publishers, New York, 1958. · Zbl 0084.10402
[8] LIPECKI Z.: Math. Review 85b: 46049. · Zbl 1236.46009 · doi:10.4064/ba59-2-7
[9] SWARTZ, CH.: Integrability for the Dobrakov integral. Czech. Math. J. 30(105), 1980, 640-646. · Zbl 0506.28005 · eudml:13230
[10] SWARTZ, CH.: Integrating bounded functions for the Dobrakov integral. Math. Slovaca 33, 1983, 141-144. · Zbl 0518.28004 · eudml:31553
[11] SWARTZ, CH.: Correction to [10]. Math. Slovaca 35, 1985, 98.
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