| 来源类型 | Article
|
| 规范类型 | 其他
|
| On a density property of weakly absolutely continuous measures. General case. |
| [unavailable]
|
| 发表日期 | 2017
|
| 出处 | Izvestiya Instituta Matematiki i Informatiki 2 (50): 3-12.
|
| 出版年 | 2017
|
| 语种 | 英语
|
| 摘要 | It is shown that some set of all step functions (and the set of all uniform limits of such functions) allows an embedding into a compact subset (with respect to weak-star topology) of the set of all finitely additive measures of bounded variation in the form of an everywhere dense subset. In particular, we consider the set of all step functions (the set of all uniform limits of such functions) such that an integral of absolute value of the functions with respect to nonnegative finitely additive measure λ is equal to unity. For these sets, the possibility of embedding is proved without any additional assumptions on λ; this generalizes the previous results. Using the Sobczyk-Hammer decomposition theorem, we show that for λ with the finite range, the above-mentioned sets of functions allow an embedding into the unit sphere (in the strong norm-variation) of weakly absolutely continuous measures with respect to λ in the form of an everywhere dense subset. For λ with an infinite range, the above-mentioned sets of functions allow an embedding into the unit ball of weakly absolutely continuous measures with respect to λ in the form of an everywhere dense subset. The results can be helpful for an extension of linear impulse control problems in the class of finitely additive measures to obtain robust representations of reachable sets given by constraints of asymptotic character. |
| 主题 | Advanced Systems Analysis (ASA)
|
| 关键词 | finitely additive measures, weak absolute continuity, weak-star topology, nonatomic or atomless measures, Sobczyk-Hammer decomposition
|
| URL | http://pure.iiasa.ac.at/id/eprint/15046/
|
| 来源智库 | International Institute for Applied Systems Analysis (Austria)
|
| 资源类型 | 智库出版物
|
| 条目标识符 | http://119.78.100.153/handle/2XGU8XDN/130835
|
推荐引用方式
GB/T 7714 |
[unavailable]. On a density property of weakly absolutely continuous measures. General case.. 2017.
|
|
文件名：
|
50-01.pdf
|
|
格式：
|
Adobe PDF
|
此文件暂不支持浏览
除非特别说明，本系统中所有内容都受版权保护，并保留所有权利。
