On the extremality of regular extensions of contents and measures
Commentationes Mathematicae Universitatis Carolinae (1995)
- Volume: 36, Issue: 2, page 213-218
- ISSN: 0010-2628
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topAdamski, Wolfgang. "On the extremality of regular extensions of contents and measures." Commentationes Mathematicae Universitatis Carolinae 36.2 (1995): 213-218. <http://eudml.org/doc/247718>.
@article{Adamski1995,
abstract = {Let $\mathcal \{A\}$ be an algebra and $\mathcal \{K\}$ a lattice of subsets of a set $X$. We show that every content on $\mathcal \{A\}$ that can be approximated by $\mathcal \{K\}$ in the sense of Marczewski has an extremal extension to a $\mathcal \{K\}$-regular content on the algebra generated by $\mathcal \{A\}$ and $\mathcal \{K\}$. Under an additional assumption, we can also prove the existence of extremal regular measure extensions.},
author = {Adamski, Wolfgang},
journal = {Commentationes Mathematicae Universitatis Carolinae},
keywords = {regular content; lattice; semicompact; sequentially dominated; regular content; semicompact; sequentially dominated; lattice; extremal regular measure extensions},
language = {eng},
number = {2},
pages = {213-218},
publisher = {Charles University in Prague, Faculty of Mathematics and Physics},
title = {On the extremality of regular extensions of contents and measures},
url = {http://eudml.org/doc/247718},
volume = {36},
year = {1995},
}
TY - JOUR
AU - Adamski, Wolfgang
TI - On the extremality of regular extensions of contents and measures
JO - Commentationes Mathematicae Universitatis Carolinae
PY - 1995
PB - Charles University in Prague, Faculty of Mathematics and Physics
VL - 36
IS - 2
SP - 213
EP - 218
AB - Let $\mathcal {A}$ be an algebra and $\mathcal {K}$ a lattice of subsets of a set $X$. We show that every content on $\mathcal {A}$ that can be approximated by $\mathcal {K}$ in the sense of Marczewski has an extremal extension to a $\mathcal {K}$-regular content on the algebra generated by $\mathcal {A}$ and $\mathcal {K}$. Under an additional assumption, we can also prove the existence of extremal regular measure extensions.
LA - eng
KW - regular content; lattice; semicompact; sequentially dominated; regular content; semicompact; sequentially dominated; lattice; extremal regular measure extensions
UR - http://eudml.org/doc/247718
ER -
References
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