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Transactions of the American Mathematical Society

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Iterated limits in $ N\sp{\ast} (U\sp{n})$


Author: Carl Stephen Davis
Journal: Trans. Amer. Math. Soc. 178 (1973), 139-146
MSC: Primary 32A99
DOI: https://doi.org/10.1090/S0002-9947-1973-0315155-5
MathSciNet review: 0315155
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Abstract: It is shown that if f is in $ {N^\ast}({U^n})$, then the iterated limits of f are almost everywhere independent of the order of iteration. In fact, the iterated limit and the radial limit are equal almost everywhere.


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  • [1] A. P. Calderón and A. Zygmund, Note on the boundary values of functions of several complex variables, Contributions to Fourier Analysis, Ann. of Math. Studies, no. 25, Princeton Univ. Press, Princeton, N.J., 1950, pp. 145-165. MR 12, 19. MR 0035833 (12:19a)
  • [2] Walter Rudin, Function theory in polydiscs, Benjamin, New York, 1969. MR 41 #501. MR 0255841 (41:501)
  • [3] K. Yosida, Functional analysis, 2nd ed., Die Grundlehren der math. Wissenschaften, Band 123, Springer-Verlag, New York, 1968. MR 39 #741. MR 0239384 (39:741)
  • [4] A. Zygmund, On the boundary values of functions of several complex variables. I, Fund. Math. 36 (1949), 207-235. MR 12, 18. MR 0035832 (12:18b)
  • [5] -, Trigonometric series, 2nd ed. reprinted, Cambridge Univ. Press, New York, 1968. MR 38 #4882.

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DOI: https://doi.org/10.1090/S0002-9947-1973-0315155-5
Article copyright: © Copyright 1973 American Mathematical Society

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