Article
Keywords:
measurable multifunction; Marczewski function; Vietoris topology; simple multifunction
Summary:
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.
References:
[2] B. Kubiś:
Approximation of measurable multifunctions. To appear in Tatra Mt. Math. Publ.
MR 1771044
[4] A. Kucia, A. Nowak:
Approximation of Carathéodory type multifunctions. Bull. Polish Acad. Sci. Math. 45 (1997), 187–195.
MR 1466844
[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 0983453 |
Zbl 0705.54016
[7] A. Spakowski:
On approximation by step multifunctions without compactness conditions. Časopis Pěst. Mat. 115 (1990), 225–231.
MR 1071054 |
Zbl 0724.54017