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In this note we show that functions which preserve the property of being a lebesgue space are precisely the class of metric preserving functions.
Słowa kluczowe
Wydawca
Rocznik
Tom
Strony
249--255
Opis fizyczny
Bibliogr. 13 poz.
Twórcy
autor
- Department of Mathematics, Youngstown State University, Youngstown, OH 44555
autor
- Department of Mathematics, Slippery Rock University of PA, Slippery Rock, PA 16057
Bibliografia
- [1] Doboš, J., A survey of metric preserving functions, Questions and Answers in General Topology, Vol. 13 (1995), 129-134.
- [2] Doboš, J., On modifications of the Euclidean metric on the reals, Tatra Mountains Math. Publications., 8 (1996), 51-54.
- [3] Doboš, J., Metric Preserving Functions, Stroffek Publishers, Slovakia, 1998.
- [4] Doboš, J. and Z. Piotrowski, Some remarks on metric preserving functions, Real Analysis Exchange, 19 (1993-94), 317-320.
- [5] Jůza, M., A note on complete metric spaces, Matematicko-Fyzikálny Časopis SAV, VI, 3 (1956), 143-148 (Czech).
- [6] Levine, N., On the Lebesgue property in metric spaces, Pr. Mat., 10 (1967), 115-118.
- [7] Nadler, S. B., and T. West, A note on Lebesgue spaces, Topology Proc. Conf., Vol. 6 (1981), 363-369.
- [8] Terpe, F., Metric preserving functions of several variables, Proc. Conf. Topology and Measure V, Greifswald (1988), 169-174.
- [9] Vallin, R. W., On preserving (R, Eucl.) and almost periodic functions, Tatra Mountains Math. Publications, 24 (2002), 1-6.
- [10] Vallin, R. W., Continuity and differentiability aspects of metric preserving functions, Real Analysis Exchange, 25 (1999-2000), 849-868.
- [11] Vallin, R. W., On metric preserving functions and infinite derivatives, Acta Math. Univ. Comenianae, Vol. 67 (1998), 373-376.
- [12] Watson, S., Review of A survey of metric preserving functions, Mathematical Reviews, AMS, 96m.
- [13] Wilson, W. A., On certain types of continuous transformations of metric spaces, Amer. J. Math., 57 (1935), 62-68.
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Bibliografia
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bwmeta1.element.baztech-article-BUS2-0002-0077