Facebook Instagram Twitter RSS Feed PodBean Back to top on side

How to obtain maximal and minimal subranges of two-dimensional vector measures

In: Tatra Mountains Mathematical Publications, vol. 74, no. 2
Jerzy Legut - Maciej Wilczyński
Detaily:
Rok, strany: 2019, 85 - 90
Jazyk: eng
Kľúčové slová:
Lyapunov convexity theorem, range of a vector measure, maximal subset, maximal subrange of a vector measure.
Typ článku: mathematics
Typ dokumentu: Scientific article *.pdf
O článku:
Let $ (X, \mathcal{F}) $ be a measurable space with a nonatomic vector measure $ μ=(μ12) $. Denote by $ R(Y) $ the subrange $R(Y)=\lbrace μ(Z): Z \in \mathcal{F}, Z \subseteq Y \rbrace $. For a given $ p \in μ(\mathcal{F}) $ consider a family of measurable subsets $ \mathcal{F}p = \lbrace Z \in \mathcal{F}: μ(Z)=p \rbrace.$ Dai and Feinberg proved the existence of a maximal subset $ Z*\in \mathcal{F}p $ having the maximal subrange $ R(Z*)$ and also a minimal subset $ M* \in \mathcal{F}p $ with the minimal subrange $ R(M*)$. We present a method of obtaining the maximal and the minimal subsets. Hence, we get simple proofs of the results of Dai and Feinberg.
Ako citovať:
ISO 690:
Legut, J., Wilczyński, M. 2019. How to obtain maximal and minimal subranges of two-dimensional vector measures. In Tatra Mountains Mathematical Publications, vol. 74, no.2, pp. 85-90. 1210-3195. DOI: https://doi.org/10.2478/tmmp-2019-0022

APA:
Legut, J., Wilczyński, M. (2019). How to obtain maximal and minimal subranges of two-dimensional vector measures. Tatra Mountains Mathematical Publications, 74(2), 85-90. 1210-3195. DOI: https://doi.org/10.2478/tmmp-2019-0022
O vydaní:
Vydavateľ: Mathematical Institute, Slovak Academy of Sciences, Bratislava
Publikované: 25. 10. 2019
Verejná licencia:
Licensed under the Creative Commons Attribution-NC-ND4.0 International Public License.