- Tytuł:
- On \(\mathbb{I}\)-approximate limits and \(\mathbb{I}\)-approximate smoothness
- Autorzy:
- Zduńczyk, Rafał
- Powiązania:
- https://bibliotekanauki.pl/articles/746328.pdf
- Data publikacji:
- 2006
- Wydawca:
- Polskie Towarzystwo Matematyczne
- Tematy:
-
Density point
algebra of sets
generalized derivative - Opis:
- In this paper we present some results based on slightly modified idea of the \(\mathbb{I}\)-density introduced by Władysław Wilczyński. Some theorems are generalized versions of results from [2] and [3]. We investigate properties of functions from \(\mathbb{R}^X\), where \(X\) is supplied with the \(\mathbb{I}\)-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. \(\mathbb{I}\)-density itself does not require any structure of considered space but a metric vector space over \(\mathbb{R}\). However, in last section we confine ourselves to \(\mathbb{R}\), for we make use of \(\mathbb{R}\)’s structure for simplicity. To find more about related topics see [4], [5], more bibliography one can find in [1] and [5].
- Źródło:
-
Commentationes Mathematicae; 2006, 46, 1
0373-8299 - Pojawia się w:
- Commentationes Mathematicae
- Dostawca treści:
- Biblioteka Nauki
Artykuł