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Transactions of the American Mathematical Society

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Seminorms and the Egoroff property in Riesz spaces


Author: John A. R. Holbrook
Journal: Trans. Amer. Math. Soc. 132 (1968), 67-77
MSC: Primary 46.06
DOI: https://doi.org/10.1090/S0002-9947-1968-0228979-8
MathSciNet review: 0228979
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  • [1] S. Banach and C. Kuratowski, Sur une généralisation du problème de mesure, Fund. Math. 14 (1929), 127-131.
  • [2] N. Bourbaki, Eléments de mathématique. XIII. Première partie: Les structures fondamentales de l’analyse. Livre VI: Intégration. Chapitre I: Inégalités de convexité. Chapitre II: Espaces de Riesz. Chapitre III: Mesures sur les espaces localement compacts. Chapitre IV: Prolongement d’une mesure; espaces 𝐿^{𝑝}, Actualités Sci. Ind., no. 1175, Hermann et Cie, Paris, 1952 (French). MR 0054691
  • [3] D. T. Egoroff, Sur les suites des fonctions mesurables, C. R. Acad. Sci. Paris 152 (1911), 244-246.
  • [4] Kurt Gödel, The Consistency of the Continuum Hypothesis, Annals of Mathematics Studies, no. 3, Princeton University Press, Princeton, N. J., 1940. MR 0002514
  • [5] Shozo Koshi, On semi-continuity of functionals. I, Proc. Japan. Acad. 34 (1958), 513–517. MR 0100778
  • [6] W. A. J. Luxemburg and A. C. Zaanen, Notes on Banach function spaces, Proc. Acad. Sci. Amsterdam; Note I, A66 (1963), 135-147; Note II, A66, 148-153; Note III, A66, 239-250; Note IV, A66, 251-263; Note V, A66, 496-504; Note VI, A66, 655-668; Note VII, A66, 669-681; Note VIII, A67 (1964), 104-119; Note IX, A67, 360-376; Note X, A67, 493-506; Note XI, A67, 507-518; Note XII, A67, 519-529; Note XIII, A67, 530-543.
  • [7] W. A. J. Luxemburg, Notes on Banach function spaces, Proc. Acad. Sci. Amsterdam : Note XIV, A68 (1965), 229-248; Note XV, A68, 415-446; Note XVI, A68, 646-667.
  • [8] W. A. J. Luxemburg, On finitely additive measures in Boolean algebras, J. Reine Angew. Math. 213 (1963/1964), 165–173. MR 0163859, https://doi.org/10.1515/crll.1964.213.165
  • [9] -, Non-standard analysis, 2nd ed., California Inst. of Tech., Pasadena, Calif., 1964.
  • [10] Hidegorô Nakano, Modulared Semi-Ordered Linear Spaces, Maruzen Co., Ltd., Tokyo, 1950. MR 0038565
  • [11] W. Sierpiński, Hypothèse du continu, Monogr. Mat., Warsaw, 1934.

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DOI: https://doi.org/10.1090/S0002-9947-1968-0228979-8
Article copyright: © Copyright 1968 American Mathematical Society