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On some classical measure-theoretic theorems for non-sigma-complete Boolean algebras

Seria
Rozprawy Matematyczne tom/nr w serii: 214 wydano: 1982
Zawartość
Warianty tytułu
Abstrakty
EN

CONTENTS
Introduction...................................................................................5
§1. Preliminaries...........................................................................7
§2. Definitions and a theorem of Diestel, Faires and Huff.............9
§3. Examples...............................................................................13
§4. Some special classes of Boolean algebras ..........................19
§5. The Grothendieck property...................................................22
§6. The Orlicz-Pettis property ....................................................27
References.................................................................................32
Słowa kluczowe
Tematy
Miejsce publikacji
Warszawa
Copyright
Seria
Rozprawy Matematyczne tom/nr w serii: 214
Liczba stron
34
Liczba rozdzia³ów
Opis fizyczny
Dissertationes Mathematicae, Tom CCXIV
Daty
wydano
1982
Twórcy
Bibliografia
  • [A 62] D. Amir, Continuous function spaces with the bounded extension property, Bull. Res. Council Israel, Sect. F. 10(1962), pp. 133-138.
  • [A 61] T. Andô, Convergent sequences of finitely additive measures. Pacific J. Math. 11 (1961), pp. 395-404.
  • [B-H 76] A. Broughton and B. W. Huff, A comment of unions of σ-fields, preprint from Queens Univ., Kingston, Canada.
  • [C 78] J. B. Cooper, Saks spaces and applications to functional analysis. North Holland, Amsterdam 1978.
  • [D 78] F. K. Dashiell, Non-weakly compact operators from semi-complete C(S)-lattices and applications to Baire-classes, Trans. Amer. Math. Soc. 266 (1981), pp. 397-413.
  • [D 73] J. Diestel, Grothendieck spaces and vector measures, in Vector and Operator Valued Measures and Applications, Academic Press, New York 1973, pp. 97-108.
  • [D-F-H 76] J. Diestel, B. Faires and R. Huff, Convergence and Boundedness of Measures on non-sigma complete Algebras, preprint.
  • [D-S 78] J. Diestel and C. Seifert, The Banach-Saks Ideal I. Operators acting on C(Ω), Commentationes Mathematicae, Tomus Specialis in Honorem Ladislai Orlicz, vol. I, pp. 109-118, PWN, Warszawa 1978; vol. II, pp. 343-344 (errata), PWN, Warszawa 1979.
  • [D-U 77] J. Diestel and J.J. Uhl, Vector measures, Mathematical surveys of the A.M.S. 15, 1977.
  • [D 76] L. Drewnowski, An extension of a theorem of Rosenthal on operators acting from $l^{∞}(Γ)$, Studia Math. 57(1976), pp. 109-215.
  • [D 72] L. Drewnowski, Topological rings of sets, continuous set functions, integration II, Bull. Acad. Polon. Sci. 20 (1972), pp. 277-286.
  • [D-S 58] N. Dunford, J. Schwartz, Linear Operators, part I, Interscience Publishers, New York 1958.
  • [F 76] B. Faires, On Vitali-Hahn-Nikodym type theorems, Ann. Inst. Fourier, Grenoble, 26.4(1976), pp. 99-114.
  • [G 53] A. Grothendieck, Sur les applications linéaires faiblement compactes d'espaces du type C(K), Canad. J. Math. 5 (1953), pp. 129-173.
  • [H 63] P. Halmos, Lectures on Boolean Algebras, Van Nostrand Math. Studies No. 1, Princeton 1963.
  • [H 79] R. Haydon, A non-reflexive Grothendieck Space that does not contain $l^{∞}$ (to appear).
  • [I-S 63] J. R. Isbell and Z. Semadeni, Projection constants and spaces of continuous functions, Trans. Amer. Math. Soc. 107(1963), pp. 38-48.
  • [J 74] G. J. O. Jameson, Topology and normed spaces, Chapman and Hall, London 1974.
  • [K 77] G. Köthe, Topological Vector Spaces II, Springer, 1977.
  • [L 64] J. Lindenstrauss, On the extension of operators with range in a C(K)-space, Proc. Amer. Math. Soc. 15(1964), pp. 218-225.
  • [P 68] A. Pełczyński, On Banach spaces containing L¹(μ), Studia Math. 30(1968), pp. 231-246.
  • [R 70] H. P. Rosenthal, On relatively disjoint families of measures with some applications to Banach-space theory, ibid. 37(1970), pp. 13-36.
  • [S 71] H.H. Scheafer, Topological Vector Spaces, Springer, 1971.
  • [S 68] G. L. Seever, Measures on F-spaces, Trans. Amer. Math. Soc. 133(1968), pp. 267-280.
  • [S 71,a] Z. Semadeni, Banach spaces of continuous functions, PWN, Warsaw 1971.
  • [S 62] R. Sikorski, Boolean Algebras, Ergebnisse der Math., Band 25, Springer Verlag, Berlin 1962.
  • [T 79] M. Talagrand, Use of the Continuum Hypothesis in the construction of compact spaces (to appear).
Języki publikacji
EN
Uwagi
ERRATA

Page, line: 6¹
For: barelled Read: barrelled

Page, line: 6¹²
For: coordinate Read: coordinate)

Page, line: 6₇
For: barreled Read: barrelled

Page, line: 7₁₁
For: Bodean algebra Read: Boolean algebra

Page, line: 9¹⁵
For: Randon-measure Read: Radon-measure

Page, line: 17₆
For: concides Read: coincides

Page, line: 25₁
For: j* Read: j⁎

Page, line: 29³ˑ⁵
For: $x_{m_j}$ Read: $x_{m̅_j}$
Identyfikator YADDA
bwmeta1.element.zamlynska-46047466-7a42-41f0-b7cf-c4e008ff3e05
Identyfikatory
ISBN
83-01-03451-3
ISSN
0012-3862
Kolekcja
DML-PL
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