Products and projective limits of function spaces

Miroslav Kačena

Commentationes Mathematicae Universitatis Carolinae (2008)

  • Volume: 49, Issue: 4, page 547-578
  • ISSN: 0010-2628

Abstract

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We introduce a notion of a product and projective limit of function spaces. We show that the Choquet boundary of the product space is the product of Choquet boundaries. Next we show that the product of simplicial spaces is simplicial. We also show that the maximal measures on the product space are exactly those with maximal projections. We show similar characterizations of the Choquet boundary and the space of maximal measures for the projective limit of function spaces under some additional assumptions and we prove that the projective limit of simplicial spaces is simplicial.

How to cite

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Kačena, Miroslav. "Products and projective limits of function spaces." Commentationes Mathematicae Universitatis Carolinae 49.4 (2008): 547-578. <http://eudml.org/doc/250474>.

@article{Kačena2008,
abstract = {We introduce a notion of a product and projective limit of function spaces. We show that the Choquet boundary of the product space is the product of Choquet boundaries. Next we show that the product of simplicial spaces is simplicial. We also show that the maximal measures on the product space are exactly those with maximal projections. We show similar characterizations of the Choquet boundary and the space of maximal measures for the projective limit of function spaces under some additional assumptions and we prove that the projective limit of simplicial spaces is simplicial.},
author = {Kačena, Miroslav},
journal = {Commentationes Mathematicae Universitatis Carolinae},
keywords = {Choquet theory; function space; product; projective limit; simplicial space; Choquet theory; function space; product; projective limit; simplicial space},
language = {eng},
number = {4},
pages = {547-578},
publisher = {Charles University in Prague, Faculty of Mathematics and Physics},
title = {Products and projective limits of function spaces},
url = {http://eudml.org/doc/250474},
volume = {49},
year = {2008},
}

TY - JOUR
AU - Kačena, Miroslav
TI - Products and projective limits of function spaces
JO - Commentationes Mathematicae Universitatis Carolinae
PY - 2008
PB - Charles University in Prague, Faculty of Mathematics and Physics
VL - 49
IS - 4
SP - 547
EP - 578
AB - We introduce a notion of a product and projective limit of function spaces. We show that the Choquet boundary of the product space is the product of Choquet boundaries. Next we show that the product of simplicial spaces is simplicial. We also show that the maximal measures on the product space are exactly those with maximal projections. We show similar characterizations of the Choquet boundary and the space of maximal measures for the projective limit of function spaces under some additional assumptions and we prove that the projective limit of simplicial spaces is simplicial.
LA - eng
KW - Choquet theory; function space; product; projective limit; simplicial space; Choquet theory; function space; product; projective limit; simplicial space
UR - http://eudml.org/doc/250474
ER -

References

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