2010 Fiscal Year Final Research Report
New smoothness conditions on Riesz spaces with applications to nonadditive measures and Choquet integrals
| Project/Area Number |
20540163
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| Research Category |
Grant-in-Aid for Scientific Research (C)
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| Allocation Type | Single-year Grants |
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| Section | 一般 |
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| Research Field |
Basic analysis
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| Research Institution | Shinshu University |
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Principal Investigator |
KAWABE Jun Shinshu University, 工学部, 教授 (50186136)
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| Co-Investigator(Renkei-kenkyūsha) |
KIMURA Morishige 信州大学, 工学部, 教授 (00026345)
TAKANO Kazuhiko 信州大学, 全学教育機構, 教授 (80252063)
YAMASAKI Motohiro (30021017)
OHNO Hiromichi 信州大学, 工学部, 准教授 (90554585)
SUZUKI Akito 信州大学, 工学部, 助教 (70585611)
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| Project Period (FY) |
2008 – 2010
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| Keywords | 非加法的測度 / ショケ積分 / リース空間 / 漸近的エゴロフ性 / 多重エゴロフ性 / 単調関数連続性条件 / ショケ積分の収束定理 / 歪直積測度 |
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| Research Abstract |
It is well known that the ε-δargument plays an important role in the proof of many theorems in nonadditive measure theory and in Choquet integration theory. That is why new concepts and techniques for proving are required to develop these studies for Riesz space-valued nonadditive measures. In this research, Riesz space-valued nonadditive measure theory and their Choquet integration thoery are developed with the help of new smoothness conditions on Riesz spaces such as the asymptotic Egoroff property, the multiple Egoroff property, and the monotone function continuity property.
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