2013 Fiscal Year Final Research Report
Topological Structure of Weak Convergence of Nonadditive Measures
| Project/Area Number |
23540192
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| Research Category |
Grant-in-Aid for Scientific Research (C)
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| Allocation Type | Multi-year Fund |
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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 信州大学, 工学部, 教授 (50186136)
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| Project Period (FY) |
2011 – 2013
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| Keywords | 非加法的測度 / 測度の弱収束 / レビ収束 / ショケ積分 / 同程度一様自己連続 / ショケ積分表示問題 / 漸近平行移動可能性 / 共単調加法性 |
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| Research Abstract |
We introduced two explicit metrics for nonadditive measures on a metric space, which are called the Levy-Prokhorov metric and the Fortet-Mourier metric, and investigated their basic properties. Then, we gave a notion of the uniform equi-autocontinuity for a set of nonadditive measures and showed that both the Levy topology and the weak topology have uniform structures on such a set. As a result, we revealed that the Levy topology and the weak topology can be metrized by those explicit metrics.
Next, we introduced an asymptotically translatable condition for a nonlinear functional to solve a Choquet integral representation problem for a comonotonically additive, monotone functional on the space of all continuous functions with compact support on a locally compact space.
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