Lower density operators. Φf versus Φd

• Autorzy: Ivanova Gertruda , Wagner-Bojakowska Elżbieta , Wilczyński Władysław

Identyfikatory

DOI

10.7494/OpMath.2023.43.2.185

• Języki publikacji: EN

Abstrakty

EN

Using the new method of the construction of lower density operator introduced in the earlier paper of the first two authors, we study how much the new operator can be different from the classical one. The aim of this paper is to show that if f is a good adjusted measure-preserving bijection then the lower density operator generated by f can be really different from the classical density operator.

Słowa kluczowe

EN

lower density operator; measure-preserving bijection

• Wydawca: AGH University of Science and Technology Press
• Czasopismo: Opuscula Mathematica
• Rocznik: 2023
• Tom: Vol. 43, no. 2
• Strony: 185--197
• Opis fizyczny: Bibliogr. 9 poz.

Twórcy

autor

Ivanova Gertruda

• Pomeranian University in Słupsk, Institute of Exact and Technical Sciences, Arciszewskiego 22d, 76-200 Słupsk, Poland

• https://orcid.org/0000-0002-1832-9491

autor

Wagner-Bojakowska Elżbieta

• Łódź University, Faculty of Mathematics and Computer Science, Stefana Banacha 22, 90-238 Łódź, Poland

• https://orcid.org/0000-0002-5916-6481

autor

Wilczyński Władysław

• Łódź University, Faculty of Mathematics and Computer Science, Stefana Banacha 22, 90-238 Łódź, Poland

• https://orcid.org/0000-0002-7478-9847

Bibliografia

• [1] A.M. Bruckner, Differentiation of Real Functions, Lecture Notes in Mathematics, vol. 659, Springer-Verlag, Berlin, 1978.
• [2] A. Denjoy, Leçons sur le Calcul des Coefficients d’une Série Trigonométrique. Tome I. La Différentiation Seconde Mixte et Son Application aux Séries Trigonométriques, Gauthier-Villars, Paris, 1941.
• [3] C. Goffman, C. Neugebauer, T. Nishiura, Density topology and approximate continuity, Duke Math. J. 28 (1961), 497–505.
• [4] C. Goffman, D. Waterman, Approximately continuous transformations, Proc. AMS 12 (1961), 116–121.
• [5] G. Ivanova, E. Wagner-Bojakowska, On lower density operators, submitted.
• [6] J. Lukeš, J. Malý, L. Zajiček, Fine Topology Methods in Real Analysis and Potential Theory, Lecture Notes in Mathematics, vol. 1189, Springer-Verlag, 1986.
• [7] J.C. Oxtoby, Measure and Category, Springer-Verlag, New York, 1971.
• [8] W. Wilczyński, Density topologies, [in:] E. Pap (ed.), Handbook of Measure Theory, vol. I and II, Amsterdam, North-Holland, 2002, 675–702.
• [9] L. Zajíček, Porosity and σ-porosity, Real Anal. Exchange 13 (1987/88), 314–350.

Uwagi

Opracowanie rekordu ze środków MEiN, umowa nr SONP/SP/546092/2022 w ramach programu "Społeczna odpowiedzialność nauki" - moduł: Popularyzacja nauki i promocja sportu (2022-2023)