Affine Baire functions on Choquet simplices

Miroslav Kačena; Jiří Spurný

Open Mathematics (2011)

  • Volume: 9, Issue: 1, page 127-138
  • ISSN: 2391-5455

Abstract

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We construct a metrizable simplex X such that for each n ɛ ℕ there exists a bounded function f on ext X of Baire class n that cannot be extended to a strongly affine function of Baire class n. We show that such an example cannot be constructed via the space of harmonic functions.

How to cite

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Miroslav Kačena, and Jiří Spurný. "Affine Baire functions on Choquet simplices." Open Mathematics 9.1 (2011): 127-138. <http://eudml.org/doc/269094>.

@article{MiroslavKačena2011,
abstract = {We construct a metrizable simplex X such that for each n ɛ ℕ there exists a bounded function f on ext X of Baire class n that cannot be extended to a strongly affine function of Baire class n. We show that such an example cannot be constructed via the space of harmonic functions.},
author = {Miroslav Kačena, Jiří Spurný},
journal = {Open Mathematics},
keywords = {Baire functions; Compact convex sets; Simplex; Affine classes; Harmonic functions; compact convex sets; simplex; affine classes; harmonic functions},
language = {eng},
number = {1},
pages = {127-138},
title = {Affine Baire functions on Choquet simplices},
url = {http://eudml.org/doc/269094},
volume = {9},
year = {2011},
}

TY - JOUR
AU - Miroslav Kačena
AU - Jiří Spurný
TI - Affine Baire functions on Choquet simplices
JO - Open Mathematics
PY - 2011
VL - 9
IS - 1
SP - 127
EP - 138
AB - We construct a metrizable simplex X such that for each n ɛ ℕ there exists a bounded function f on ext X of Baire class n that cannot be extended to a strongly affine function of Baire class n. We show that such an example cannot be constructed via the space of harmonic functions.
LA - eng
KW - Baire functions; Compact convex sets; Simplex; Affine classes; Harmonic functions; compact convex sets; simplex; affine classes; harmonic functions
UR - http://eudml.org/doc/269094
ER -

References

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