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

• Autorzy: Artur Michalak
• Języki publikacji: 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.

Kategorie tematyczne

• 46B20: Geometry and structure of normed linear spaces
• 28A78: Hausdorff and packing measures

• Wydawca: Institute of Mathematics Polish Academy of Sciences
• Czasopismo: Bulletin of the Polish Academy of Sciences. Mathematics
• Rocznik: 2014
• Tom: 62
• Numer: 1
• Strony: 61-76

Daty

wydano

2014

Twórcy

autor

Artur Michalak

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

Identyfikatory

DOI

10.4064/ba62-1-7