Functions which preserve Lebesgue spaces

• Autorzy: Piotrowski Z. , Vallin R. W.
• Języki publikacji: EN

Abstrakty

EN

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

EN

Lebesgue space; metric preserving functions

• Wydawca: Polskie Towarzystwo Matematyczne
• Czasopismo: Annales Societatis Mathematicae Polonae. Seria 1: Commentationes Mathematicae
• Rocznik: 2003
• Tom: [Z] 43(2)
• Strony: 249--255
• Opis fizyczny: Bibliogr. 13 poz.

Twórcy

autor

Piotrowski Z.

• Department of Mathematics, Youngstown State University, Youngstown, OH 44555

autor

Vallin R. W.

• 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.