Pełnotekstowe zasoby PLDML oraz innych baz dziedzinowych są już dostępne w nowej Bibliotece Nauki.
Zapraszamy na https://bibliotekanauki.pl

PL EN

Preferencje
Język
Widoczny [Schowaj] Abstrakt
Liczba wyników
• # Artykuł - szczegóły

## Bulletin of the Polish Academy of Sciences. Mathematics

2014 | 62 | 1 | 61-76

## On Some Properties of Separately Increasing Functions from [0,1]ⁿ into a Banach Space

EN

### Abstrakty

EN
We say that a function f from [0,1] to a Banach space X is increasing with respect to E ⊂ X* if x* ∘ f is increasing for every x* ∈ E. A function $f:[0,1]^m → X$ is separately increasing if it is increasing in each variable separately. We show that if X is a Banach space that does not contain any isomorphic copy of c₀ or such that X* is separable, then for every separately increasing function $f:[0,1]^m → X$ with respect to any norming subset there exists a separately increasing function $g:[0,1]^m → ℝ$ such that the sets of points of discontinuity of f and g coincide.

61-76

wydano
2014

### Twórcy

autor
• Faculty of Mathematics and Computer Science, Adam Mickiewicz University, Umultowska 87, 61-614 Poznań, Poland