A stabilization property and its applications in the theory of sections
Séminaire Choquet. Initiation à l'analyse (1977)
- Volume: 17, Issue: 1, page 1-23
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topBourgain, Jean. "A stabilization property and its applications in the theory of sections." Séminaire Choquet. Initiation à l'analyse 17.1 (1977): 1-23. <http://eudml.org/doc/110561>.
@article{Bourgain1977,
author = {Bourgain, Jean},
journal = {Séminaire Choquet. Initiation à l'analyse},
keywords = {descriptive set theory; paving; Souslin schemes; stabilization property; separation theorem; Borel sets; Baire property; Lebesgue measurable sets; sections; Borel subsets of a Polish topological space},
language = {eng},
number = {1},
pages = {1-23},
publisher = {Secrétariat mathématique},
title = {A stabilization property and its applications in the theory of sections},
url = {http://eudml.org/doc/110561},
volume = {17},
year = {1977},
}
TY - JOUR
AU - Bourgain, Jean
TI - A stabilization property and its applications in the theory of sections
JO - Séminaire Choquet. Initiation à l'analyse
PY - 1977
PB - Secrétariat mathématique
VL - 17
IS - 1
SP - 1
EP - 23
LA - eng
KW - descriptive set theory; paving; Souslin schemes; stabilization property; separation theorem; Borel sets; Baire property; Lebesgue measurable sets; sections; Borel subsets of a Polish topological space
UR - http://eudml.org/doc/110561
ER -
References
top- [1] Arsenin ( W.J.), Ljapuncv ( A.A.), Čegolkov ( E.A.). - Arbeiten zur deskriptiven Mengenlehre. - Berlin VEB Deutscher Verlag der Wissenschaften, 1955 (Mathematische Forschungsberichte, 1). Zbl0068.27001MR73660
- [2] Baire ( R.). - Sur les fonctions des variables réelles, Annali Mat. pura ed appl., 3e Série, t. 3, 1899, p. 1-123 (Thèse Sc. math.). JFM30.0359.01
- [3] Bourbaki ( N.). - Intégration. Chap. 1-8. - Paris, Hermann, 1956-1965 (Act. scient. et ind., 1175, 1244, 1306 ; Bourbaki, 13, 21, 29).
- [4] Bourgain ( J.). - Decompositions in the product of a measure space and a polish space (submitted to Fundamenta Mathematicae). Zbl0419.28001
- [5] Bourgain ( J.), Fremlin ( D.H.) and Talagrand ( M.). - Pointwise compact sets of Baire measurable functions (submitted to Amer. J. Math.). Zbl0413.54016MR509077
- [6] Christensen ( J.P.R.). - Topology and Borel structure. - Amsterdam, North-Holland Publishing Company, 1974 (North-Holland Mathematics Studies, 10 ; Notas de Matematica, 51). Zbl0273.28001MR348724
- [7] Čoban ( M.M.). - On B-measurable sections, Soviet Math. Dokl., t. 13, 1972, p. 1473-1477. Zbl0284.54009MR322790
- [8] Dellacherie ( C.). - Capacités et processus stochastiques. - Berlin, Springer-Verlag, 1972 (Ergebnisse der Mathematik, 67). Zbl0246.60032MR448504
- [9] Dellacherie ( C.). - Ensembles analytiques, capacités, mesures de Hausdorff. - Berlin, Springer-Verlag, 1972 (Lecture Notes in mathematics, 295). Zbl0259.31001MR492152
- [10] Dellacherie ( C.). - Ensembles analytiques : Théorèmes de separation et applications. - Berlin, Heidelberg, New York, Springer-Verlag, 1975 (Lecture Notes in Mathematics, 465). Zbl0354.54023MR428306
- [11] Dellacherie ( C.). - Une démonstration du théorème de Souslin-Lusin, "Séminaire de probabilités de l'Université de Strasbourg, VII, Année 1971/72", p. 48-50. - Berlin, Springer-Verlag, 1973 (Lecture Notes in Mathematics, 321). Zbl0261.54030MR383375
- [12] Effros ( E.G.). - Convergence of closed subsets in a topological space, Proc. amer. Math. Soc., t. 16, 1965, p. 929-931. Zbl0139.40403MR181983
- [13] Halmos ( P.R.). - Measure theory. - Toronto, D. Van Nostrand Company, 1950 (The University Series in higher Mathematics). Zbl0040.16802MR33869
- [14] Hausdorff ( F.). - Set theory. - New York, Chelsea Publishing Company, 1962. Zbl0488.04001MR141601
- [15] Hoffmann-Jørgensen ( J.). - The theory of analytic spaces. - Aarhus, Aarhus Universitet, Mathematik Inst., 1970 (Various Publication Series, 10). Zbl0226.28001MR409748
- [16] Hurewicz ( W.). - Relativ perfekte Teile von Punktmengen und Mengen (A), Fund. Math., Warszawa, t. 12, 1928, p. 78-109. Zbl54.0097.06JFM54.0097.06
- [17] Jech ( T.J.). - Lectures in set theory with particular emphasis on the method of forcing. - Berlin, Springer-Verlag, 1971 (Lecture Notes in Mathematics, 217). Zbl0236.02048MR321738
- [18] Kondô ( M.). - Sur l'uniformisation des complémentaires d'analytiques et les ensembles projectifs de la seconde classe, Japan. J. Math., t. 15, 1938, p. 197-230. Zbl64.1008.02JFM64.1008.02
- [19] Kunugui ( K.). - Contribution à la théorie des ensembles boréliens et analytiques, III, J. Fac. Sc. Hokkaido Univ. Serie 1, t. 8, 1939-1940, p. 79-108. Zbl0060.12905MR1818
- [20] Kuratowski ( C.). - Topologie, vol. 1 and 2, 4th edition. - PWN, Polish scientific Publishers, 1958-1961 (Monografie Matematyczne, 20, 21). Zbl0078.14603
- [21] Louveau ( Alain). - La hiérarchie borélienne des ensembles Δ11, C. R. Acad. Sc. Paris, t. 285, 1977, Série A, p. 601-604. Zbl0363.04008
- [22] Martin ( D.A.) and Solovay ( R.M.). - Internal Cohen extensions, Ann. of math. logic, t. 2, 1970, p. 143-178. Zbl0222.02075MR270904
- [23] Meyer ( P.-A.). - Probabilités et potentiels. - Paris, Hermann, 1966 (Act. scient. et ind., 1318 ; Publ. Inst. Math. Univ. Strasbourg, 14). Zbl0138.10402MR205287
- [24] Novikov ( P.). - The separation of CA sets, Izv. Akad. Nauk SSSR, Serija Mat., t. 1, 1937, p. 253-264.
- [25] Novikov ( P.). - Generalization of the second separation theorem, Doklady Akad. Nauk SSSR, t. 4, 1934, p. 8-11. Zbl0010.15504
- [26] Purves ( R.). - Bimeasurable functions, Fund. Math., Warszawa, t. 58, 1966, p. 149-157. Zbl0143.07101MR199339
- [27] Rogers ( C.A.). - Lusin's second theorem of separation, J. London, math. Soc., 2nd Serie, t. 6, 1973, p. 491-503. Zbl0256.04003MR377839
- [28] Schwartz ( L.). - Radon measures on Souslin spaces, "Symposium on analysis [1967, Kingston]", p. 157-168. - Kingston, Queen's University, 1967 (Queen's Papers in pure and applied Mathematics, 10). Zbl0169.46801
- [29] Sierpinski ( W.). - Les ensembles projectifs et analytiques. - Paris, Gauthier-Villars, 1950 (Mémorial des Sciences mathématiques, 112). Zbl0039.04701MR52484
- [30] Sierpinski ( W.). - Sur une suite infinie de fonctions de classe 1 dont toute fonction d'accumulation est non mesurable, Fund. Math., Warszawa, t. 33, 1945, p. 104-105. Zbl0060.12712MR16443
- [31] Sierpinski ( W.). - Oeuvres choisies, Vol. 2 et 3. - Warszawa, PWN Polish scientific publishers, 1975-1976. MR414303
- [32] Solovay ( R.M.) and Tennenbaum ( S.). - Iterated Cohen extensions and Souslin's problem, Ann. of Math., 2nd serie, t. 94, 1971, p. 201-245. Zbl0244.02023MR294139
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