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Proceedings of the American Mathematical Society

Published by the American Mathematical Society since 1950, Proceedings of the American Mathematical Society is devoted to shorter research articles in all areas of pure and applied mathematics.

ISSN 1088-6826 (online) ISSN 0002-9939 (print)

The 2020 MCQ for Proceedings of the American Mathematical Society is 0.85.

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Invariance under operation $\mathcal {A}$
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by John C. Morgan and Kenneth Schilling PDF
Proc. Amer. Math. Soc. 100 (1987), 651-654 Request permission

Abstract:

The invariance under operation $\mathcal {A}$ of the families of sets having the classical Baire property, of Lebesgue measurable sets, and of Marczewski sets is established in a unified manner.
References
  • A. A. Lyapunov, On set-theoretical operations which preserve measurability, Doklady Akad. Nauk SSSR (N.S.) 65 (1949), 609–612 (Russian). MR 0028921
  • A. A. Lyapunov, On $\delta s$-operations preserving measurability and the property of Baire, Mat. Sbornik N.S. 24(66) (1949), 119–127 (Russian). MR 0028919
  • —, $R$-sets, Trudy Mat. Inst. Steklov. 40 (1953), 1-68.
  • A. A. Ljapunov, The method of transfinite indices in the theory of operations over sets, Trudy Mat. Inst. Steklov. 133 (1973), 132–148, 275 (Russian). Mathematical logic, theory of algorithms and theory of sets (dedicated to P. S. Novikov on the occasion of his seventieth birthday). MR 0366674
  • N. Lusin, Sur la classification de M. Baire, C. R. Acad. Sci. Paris 164 (1917), 91-94. —, Sur les ensembles analytiques, Fund. Math. 10 (1927), 1-95 (esp. pp. 25-28). N. Lusin and W. Sierpiński, Sur quelques propriétés des ensembles $(A)$, Bull. Intern. Acad. Sci. Cracovie (1918), 35-48. —, Sur un ensemble non mesurable $B$, J. Math. (9) 2 (1923), 53-72.
  • John C. Morgan II, On the Borel $\sigma$-field and the Baire property, Proc. Amer. Math. Soc. 90 (1984), no. 2, 250–252. MR 727243, DOI 10.1090/S0002-9939-1984-0727243-2
  • John C. Morgan II, On the general theory of point sets, Real Anal. Exchange 9 (1983/84), no. 2, 345–353. Seventh symposium on real analysis (Santa Barbara, Calif., 1984). MR 766060, DOI 10.2307/44153544
  • John C. Morgan II, Measurability and the abstract Baire property, Rend. Circ. Mat. Palermo (2) 34 (1985), no. 2, 234–244. MR 814038, DOI 10.1007/BF02850698
  • O. Nikodým, Sur une propriété de l’opération $A$, Fund. Math. 7 (1925), 149-154. —, Sur quelques propriétés de l’opération $A$, Spraw. Towarz. Nauk. Warszaw. Wyd. III 19 (1926), 294-298.
  • C. A. Rogers, Hausdorff measures, Cambridge University Press, London-New York, 1970. MR 0281862
  • S. Saks, Theory of the integral, Monografie Mat., Tom VII (2nd ed.), Hafner, New York, 1937 (esp. Chapter II, §5).
  • Kenneth Schilling and Robert Vaught, Borel games and the Baire property, Trans. Amer. Math. Soc. 279 (1983), no. 1, 411–428. MR 704624, DOI 10.1090/S0002-9947-1983-0704624-8
  • Kenneth Schilling, On absolutely $\Delta ^1_2$ operations, Fund. Math. 121 (1984), no. 3, 239–250. MR 772452, DOI 10.4064/fm-121-3-239-250
  • W. Sierpiński, Sur la mesurabilité des ensembles analytiques, Spraw. Towarz. Nauk Warszaw. Wyd. III 22 (1929), 155-159. E. Szpilrajn (Marczewski), On measurability and the Baire property, C. R. du I Congrès des Mathématiciens des Pays Slaves, Warszawa, 1929, pp. 297-303. Ksiaznica Atlas T.N.S.W., Warszawa, 1930. [English translation available from J. C. Morgan II] —, Sur certains invariants de l’opération $(A)$, Fund. Math. 21 (1933), 229-235. —, Sur une classe de fonctions de M. Sierpiński et la classe correspondante d’ensembles, Fund. Math. 24 (1935), 17-34 (esp. §2.5). —, On absolutely measurable sets and functions, Spraw. Towarz. Nauk. Warszaw. Wyd. III 30 (1937), 17-34 (esp. §2.2). [English translation available from J. C. Morgan II]
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Additional Information
  • © Copyright 1987 American Mathematical Society
  • Journal: Proc. Amer. Math. Soc. 100 (1987), 651-654
  • MSC: Primary 54H05; Secondary 28A05
  • DOI: https://doi.org/10.1090/S0002-9939-1987-0894432-9
  • MathSciNet review: 894432