Geodesic
Monotone approximation of measurable multifunctions by simple multifunctions
Mathematica Bohemica, Tome 126 (2001) no. 1, pp. 113-117

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MR Zbl
We investigate the problem of approximation of measurable multifunctions by monotone sequences of measurable simple ones. Our main tool is the Marczewski function, i.e., the characteristic function of a sequence of sets.
We investigate the problem of approximation of measurable multifunctions by monotone sequences of measurable simple ones. Our main tool is the Marczewski function, i.e., the characteristic function of a sequence of sets.
DOI : 10.21136/MB.2001.133920
Classification : 26E25, 28A20, 28B20, 54C60
Keywords: measurable multifunction; Marczewski function; Vietoris topology; simple multifunction 
Kubiś, Beata. Monotone approximation of measurable multifunctions by simple multifunctions. Mathematica Bohemica, Tome 126 (2001) no. 1, pp. 113-117. doi: 10.21136/MB.2001.133920
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[1] C. J. Himmelberg: Measurable relations. Fund. Math. 87 (1975), 53–72. | DOI | MR | Zbl

[2] B. Kubiś: Approximation of measurable multifunctions. To appear in Tatra Mt. Math. Publ. | MR

[3] A. Kucia: Some results on Carathéodory selections and extensions. J. Math. Anal. Appl. 223 (1998), 302–318. | DOI | MR | Zbl

[4] A. Kucia, A. Nowak: Approximation of Carathéodory type multifunctions. Bull. Polish Acad. Sci. Math. 45 (1997), 187–195. | MR

[5] E. Marczewski: The characteristic function of a sequence of sets and some of its applications. Fund. Math. 31 (1938), 207–223.

[6] A. Spakowski: On approximation of multifunctions with respect to the Vietoris topology. Acta Univ. Carol. Math. Phys. 29 (1988), 75–80. | MR | Zbl

[7] A. Spakowski: On approximation by step multifunctions without compactness conditions. Časopis Pěst. Mat. 115 (1990), 225–231. | MR | Zbl

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