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Dobrakov, Ivan

Remarks on the integrability in Banach spaces. (English) Zbl 0635.28005

Math. Slovaca 36, 323-327 (1986).
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)].

Cited in 6 Documents

MSC:

28B05 Vector-valued set functions, measures and integrals
46G10 Vector-valued measures and integration

Keywords:

integrating vector-valued functions with respect to operator-valued measures; Dobrakov’s integral; bounded measurable functions; integrating bounded functions

Citations:

Zbl 0518.28004
PDFBibTeX XMLCite
\textit{I. Dobrakov}, Math. Slovaca 36, 323--327 (1986; Zbl 0635.28005)
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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
[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
[4] DOBRAKOV I.: On integration in Banach spaces, II. Czech. Math. J. 20 (95), 1970, 680-695. · Zbl 0224.46050
[5] DOBRAKOV I.: On representation of linear operators on C(T, X). Czech. Math. J. 21 (96), 1971, 13-30. · Zbl 0225.47018
[6] DOBRAKOV I., FARKOVÁ J.: On submeasures II. Math. Slovaca 30, 1980, 65-81. · Zbl 0428.28001
[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
[10] SWARTZ, CH.: Integrating bounded functions for the Dobrakov integral. Math. Slovaca 33, 1983, 141-144. · Zbl 0518.28004
[11] SWARTZ, CH.: Correction to [10]. Math. Slovaca 35, 1985, 98.
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