Choquet simplexes whose set of extreme points is K -analytic

Michel Talagrand

Annales de l'institut Fourier (1985)

  • Volume: 35, Issue: 3, page 195-206
  • ISSN: 0373-0956

Abstract

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We construct a Choquet simplex K whose set of extreme points T is 𝒦 -analytic, but is not a 𝒦 -Borel set. The set T has the surprising property of being a K σ δ set in its Stone-Cech compactification. It is hence an example of a K σ δ set that is not absolute.

How to cite

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Talagrand, Michel. "Choquet simplexes whose set of extreme points is $K$-analytic." Annales de l'institut Fourier 35.3 (1985): 195-206. <http://eudml.org/doc/74683>.

@article{Talagrand1985,
abstract = {We construct a Choquet simplex $K$ whose set of extreme points $T$ is $\{\cal K\}$-analytic, but is not a $\{\cal K\}$-Borel set. The set $T$ has the surprising property of being a $K_\{\sigma \delta \}$ set in its Stone-Cech compactification. It is hence an example of a $K_\{\sigma \delta \}$ set that is not absolute.},
author = {Talagrand, Michel},
journal = {Annales de l'institut Fourier},
keywords = {Choquet simplexes whose set of extreme points is K-analytic; Stone- Čech compactification},
language = {eng},
number = {3},
pages = {195-206},
publisher = {Association des Annales de l'Institut Fourier},
title = {Choquet simplexes whose set of extreme points is $K$-analytic},
url = {http://eudml.org/doc/74683},
volume = {35},
year = {1985},
}

TY - JOUR
AU - Talagrand, Michel
TI - Choquet simplexes whose set of extreme points is $K$-analytic
JO - Annales de l'institut Fourier
PY - 1985
PB - Association des Annales de l'Institut Fourier
VL - 35
IS - 3
SP - 195
EP - 206
AB - We construct a Choquet simplex $K$ whose set of extreme points $T$ is ${\cal K}$-analytic, but is not a ${\cal K}$-Borel set. The set $T$ has the surprising property of being a $K_{\sigma \delta }$ set in its Stone-Cech compactification. It is hence an example of a $K_{\sigma \delta }$ set that is not absolute.
LA - eng
KW - Choquet simplexes whose set of extreme points is K-analytic; Stone- Čech compactification
UR - http://eudml.org/doc/74683
ER -

References

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  1. [1] G. CHOQUET, Lectures on analysis, New York, W.A. Benjamin, 1969 (Math. Lecture Notes series). Zbl0181.39602
  2. [2] Z. FROLICK, A survey of separable descriptive theory of sets and spaces, Czechoslovak Math. J., 20 (1967), 406-467. Zbl0223.54028
  3. [3] R. HAYDON, An extreme point criterion for separability of a dual Banach space, and a new proof of a theorem of Corson, Quarterly J. Math., 27 (1976), 379-385. Zbl0335.46012MR58 #12293
  4. [4] B. MACGIBBON, A criterion for the metrizability of a compact convex set in terms of the set of extreme points, J. Funct. Anal., 11 (1972), 385-392. Zbl0281.46001MR49 #7723
  5. [5] R. PHELPS, Lectures on Choquet's theorem, Van Nostrand Math. studies, 7 (1966). Zbl0135.36203MR33 #1690
  6. [6] M. TALAGRAND, Géométrie du simplexe des moyennes, J. Funct. Anal., 33 (1919), 304-333. Zbl0431.43001
  7. [7] M. TALAGRAND, Espaces de Banach faiblement K-analytiques, Ann. of Math., 110 (1979), 407-438. Zbl0393.46019MR81a:46021
  8. [8] M. TALAGRAND, Sur les convexes compacts dont l'ensemble des points extrémaux est K-analytique, Bull. Soc. Math. France, 107 (1979), 49-53. Zbl0422.46007MR80j:46023

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