# Monotone approximation of measurable multifunctions by simple multifunctions

Mathematica Bohemica (2001)

- Volume: 126, Issue: 1, page 113-117
- ISSN: 0862-7959

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topKubiś, Beata. "Monotone approximation of measurable multifunctions by simple multifunctions." Mathematica Bohemica 126.1 (2001): 113-117. <http://eudml.org/doc/248851>.

@article{Kubiś2001,

abstract = {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.},

author = {Kubiś, Beata},

journal = {Mathematica Bohemica},

keywords = {measurable multifunction; Marczewski function; Vietoris topology; simple multifunction; measurable multifunction; Marczewski function; Vietoris topology; simple multifunction},

language = {eng},

number = {1},

pages = {113-117},

publisher = {Institute of Mathematics, Academy of Sciences of the Czech Republic},

title = {Monotone approximation of measurable multifunctions by simple multifunctions},

url = {http://eudml.org/doc/248851},

volume = {126},

year = {2001},

}

TY - JOUR

AU - Kubiś, Beata

TI - Monotone approximation of measurable multifunctions by simple multifunctions

JO - Mathematica Bohemica

PY - 2001

PB - Institute of Mathematics, Academy of Sciences of the Czech Republic

VL - 126

IS - 1

SP - 113

EP - 117

AB - 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.

LA - eng

KW - measurable multifunction; Marczewski function; Vietoris topology; simple multifunction; measurable multifunction; Marczewski function; Vietoris topology; simple multifunction

UR - http://eudml.org/doc/248851

ER -

## References

top- Measurable relations, Fund. Math. 87 (1975), 53–72. (1975) Zbl0296.28003MR0367142
- Approximation of measurable multifunctions, To appear in Tatra Mt. Math. Publ. MR1771044
- Some results on Carathéodory selections and extensions, J. Math. Anal. Appl. 223 (1998), 302–318. (1998) Zbl0981.28009MR1627308
- Approximation of Carathéodory type multifunctions, Bull. Polish Acad. Sci. Math. 45 (1997), 187–195. (1997) MR1466844
- The characteristic function of a sequence of sets and some of its applications, Fund. Math. 31 (1938), 207–223. (1938)
- On approximation of multifunctions with respect to the Vietoris topology, Acta Univ. Carol. Math. Phys. 29 (1988), 75–80. (1988) Zbl0705.54016MR0983453
- On approximation by step multifunctions without compactness conditions, Časopis Pěst. Mat. 115 (1990), 225–231. (1990) Zbl0724.54017MR1071054

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