# PCA sets and convexity

Fundamenta Mathematicae (2000)

- Volume: 163, Issue: 3, page 267-275
- ISSN: 0016-2736

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topKaufman, R.. "PCA sets and convexity." Fundamenta Mathematicae 163.3 (2000): 267-275. <http://eudml.org/doc/212443>.

@article{Kaufman2000,

abstract = {Three sets occurring in functional analysis are shown to be of class PCA (also called $Σ^1_2$) and to be exactly of that class. The definition of each set is close to the usual objects of modern analysis, but some subtlety causes the sets to have a greater complexity than expected. Recent work in a similar direction is in [1, 2, 10, 11, 12].},

author = {Kaufman, R.},

journal = {Fundamenta Mathematicae},

keywords = {norm; Banach space; convex sets; integrals over extreme points; Borel set; PCA set; analytic set; co-analytic set},

language = {eng},

number = {3},

pages = {267-275},

title = {PCA sets and convexity},

url = {http://eudml.org/doc/212443},

volume = {163},

year = {2000},

}

TY - JOUR

AU - Kaufman, R.

TI - PCA sets and convexity

JO - Fundamenta Mathematicae

PY - 2000

VL - 163

IS - 3

SP - 267

EP - 275

AB - Three sets occurring in functional analysis are shown to be of class PCA (also called $Σ^1_2$) and to be exactly of that class. The definition of each set is close to the usual objects of modern analysis, but some subtlety causes the sets to have a greater complexity than expected. Recent work in a similar direction is in [1, 2, 10, 11, 12].

LA - eng

KW - norm; Banach space; convex sets; integrals over extreme points; Borel set; PCA set; analytic set; co-analytic set

UR - http://eudml.org/doc/212443

ER -

## References

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- [10] R. Kaufman, Co-analytic sets and extreme points, Bull. London Math. Soc. 19 (1987), 72-74. Zbl0601.54041
- [11] R. Kaufman, Topics on analytic sets, Fund. Math. 139 (1991), 217-229. Zbl0764.28002
- [12] R. Kaufman, Extreme points and descriptive sets, ibid. 143 (1993), 179-181. Zbl0832.54031
- [13] R. R. Phelps, Lectures on Choquet's Theorem, Van Nostrand Math. Stud. 7, Van Nostrand, Princeton, NJ, 1966. Zbl0135.36203

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