- Tytuł:
- Sierpińskis hierarchy and locally Lipschitz functions
- Autorzy:
- Morayne, Michał
- Powiązania:
- https://bibliotekanauki.pl/articles/1208370.pdf
- Data publikacji:
- 1995
- Wydawca:
- Polska Akademia Nauk. Instytut Matematyczny PAN
- Opis:
- Let Z be an uncountable Polish space. It is a classical result that if I ⊆ ℝ is any interval (proper or not), f: I → ℝ and $α < ω_1$ then f ○ g ∈ $B_α(Z)$ for every $g ∈ B_α(Z) ∩^ZI$ if and only if f is continuous on I, where $B_α(Z)$ stands for the αth class in Baire's classification of Borel measurable functions. We shall prove that for the classes $S_α(Z) (α > 0)$ in Sierpiński's classification of Borel measurable functions the analogous result holds where the condition that f is continuous is replaced by the condition that f is locally Lipschitz on I (thus it holds for the class of differences of semicontinuous functions, which is the class $S_1(Z)$). This theorem solves the problem raised by the work of Lindenbaum ([L] and [L, Corr.]) concerning the class of functions not leading outside $S_α(Z)$ by outer superpositions.
- Źródło:
-
Fundamenta Mathematicae; 1995, 147, 1; 73-82
0016-2736 - Pojawia się w:
- Fundamenta Mathematicae
- Dostawca treści:
- Biblioteka Nauki
Artykuł