Previous |  Up |  Next

Article

Keywords:
weak McShane integral; finite McShane partition; Radon measure space
Summary:
We characterize the weak McShane integrability of a vector-valued function on a finite Radon measure space by means of only finite McShane partitions. We also obtain a similar characterization for the Fremlin generalized McShane integral.
References:
[1] Bauer, H.: Measure and Integration Theory. De Gruyter Studies in Mathematics 26. Walter de Gruyter, Berlin (2001). MR 1897176 | Zbl 0985.28001
[2] Faure, C.-A., Mawhin, J.: Integration over unbounded multidimensional intervals. J. Math. Anal. Appl. 205 (1997), 65-77. DOI 10.1006/jmaa.1996.5172 | MR 1426980 | Zbl 0879.26047
[3] Fremlin, D. H.: Topological Riesz Spaces and Measure Theory. Cambridge University Press, London (1974). MR 0454575 | Zbl 0273.46035
[4] Fremlin, D. H.: The generalized McShane integral. Ill. J. Math. 39 (1995), 39-67. DOI 10.1215/ijm/1255986628 | MR 1299648 | Zbl 0810.28006
[5] Kelley, J. L., Srinivasan, T. P.: Measure and Integral Vol. 1. Graduate Texts in Mathematics 116. Springer, New York (1988). DOI 10.1007/978-1-4612-4570-4 | MR 0918770 | Zbl 0635.28001
[6] Saadoune, M., Sayyad, R.: The weak McShane integral. Czech. Math. J. 64 (2014), 387-418. DOI 10.1007/s10587-014-0108-7 | MR 3277743 | Zbl 1340.28016
[7] Schwabik, Š., Ye, G.: Topics in Banach Space Integration. Series in Real Analysis Vol. 10. World Scientific, Singapore (2005). DOI 10.1142/9789812703286 | MR 2167754 | Zbl 1088.28008
[8] Talagrand, M.: Pettis integral and measure theory. Mem. Am. Math. Soc. 307 (1984),\99999MR99999 0756174 . DOI 10.1090/memo/0307 | MR 0756174 | Zbl 0582.46049
Partner of
EuDML logo