A general realcompactification method
J. van der Slot (1970)
Fundamenta Mathematicae
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J. van der Slot (1970)
Fundamenta Mathematicae
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Frank Terpe (1971)
Colloquium Mathematicae
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J. W. Bebernes, Steven K. Ingram (1971)
Annales Polonici Mathematici
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Philip Nanzetta (1968)
Fundamenta Mathematicae
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M. A. Selby (1974)
Colloquium Mathematicae
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Doroslovački, Rade, Pantović, Jovanka, Vojvodić, Gradimir (1999)
Novi Sad Journal of Mathematics
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A. M. Stokolos (2006)
Colloquium Mathematicae
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The study of one-dimensional rare maximal functions was started in [4,5]. The main result in [5] was obtained with the help of some general procedure. The goal of the present article is to adapt the procedure (we call it "dyadic crystallization") to the multidimensional setting and to demonstrate that rare maximal functions have properties not better than the Strong Maximal Function.
Petr Simon (1971)
Commentationes Mathematicae Universitatis Carolinae
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Nakaoka, Fumie, Oda, Nobuyuki (2003)
International Journal of Mathematics and Mathematical Sciences
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J. Van der Slot (1969)
Compositio Mathematica
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Andrey V. Koldunov, Aleksandr I. Veksler (2001)
Commentationes Mathematicae Universitatis Carolinae
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In [5] the following question was put: are there any maximal n.d. sets in ? Already in [9] the negative answer (under ) to this question was obtained. Moreover, in [9] it was shown that no -set can be maximal n.d. In the present paper the notion of a maximal n.d. -set is introduced and it is proved that under there is no such a set in . The main results are Theorem 1.10 and especially Theorem 2.7(ii) (with Example in Section 3) in which the problem of the existence of maximal n.d....