On II-approximate limits and II-approximate smoothness

• Autorzy: Zduńczyk R.
• Języki publikacji: EN

Abstrakty

EN

In this paper we present some results based on slightly modified idea of the I-density introduced by Władysław Wilczyński. Some theorems are generalized versions of results from [2] and [3]. We investigate properties of functions from R^X, where X is supplied with the I-density. We try to free our considerations from the assumption of Baire property, or measurability. In some cases this is not done yet. Star-marked statements still need that assumption, proofs presented here are done for Baire property, but it is possible to adapt them to measure. I-density itself does not require any structure of considered space but a metric vector space over R. However, in last section we confine ourselves to R, for we make use of R’s structure for simplicity. To find more about related topics see [4], [5], more bibliography one can find in [1] and [5].

Słowa kluczowe

EN

density points; algebra of sets; generalized derivative

• Wydawca: Polskie Towarzystwo Matematyczne
• Czasopismo: Annales Societatis Mathematicae Polonae. Seria 1: Commentationes Mathematicae
• Rocznik: 2006
• Tom: Vol. 46, [Z] 1
• Strony: 1--16
• Opis fizyczny: bibliogr. 4 poz.

Twórcy

autor

Zduńczyk R.

• Uniwersytet Łódzki, Wydział Matematyki Banacha 22, Łódz, Poland,

Bibliografia

• [1] K. Ciesielski., L. Larson and K. Ostaszewski, I-Density Continuous Functions, Memoirs of the AMS, vol. 107, no. 515, 1994.
• [2] J. M. Jędrzejewski, Funkcje aproksymatywnie gładkie, Zesz. Nauk. UŁ, seria 2, zeszyt 52, Łódz, (1973) 7-14.
• [3] J. M. Jedrzejewski, O granicy i ciągłości uogólnionej, Zesz. Nauk. UŁ, seria 2, zeszyt 52, Łódz, 1973, 19-38.
• [4] M. Strześniewski, On I-Assymetry, Real Analysis Exchange, Vol. 26(2), (2001), 593-602.
• [5] W. Wilczyński, Density Topologies, HANDBOOK OF MEASURE THEORY, Elsevier Science B. V., 2002, 675-702.