Monotone approximation of measurable multifunctions by simple multifunctions

Beata Kubiś

Mathematica Bohemica (2001)

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

Abstract

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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.

How to cite

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Kubiś, 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

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

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