| Budget Amount *help |
¥4,550,000 (Direct Cost: ¥3,500,000、Indirect Cost: ¥1,050,000)
Fiscal Year 2022: ¥910,000 (Direct Cost: ¥700,000、Indirect Cost: ¥210,000)
Fiscal Year 2021: ¥910,000 (Direct Cost: ¥700,000、Indirect Cost: ¥210,000)
Fiscal Year 2020: ¥910,000 (Direct Cost: ¥700,000、Indirect Cost: ¥210,000)
Fiscal Year 2019: ¥910,000 (Direct Cost: ¥700,000、Indirect Cost: ¥210,000)
Fiscal Year 2018: ¥910,000 (Direct Cost: ¥700,000、Indirect Cost: ¥210,000)
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| Outline of Final Research Achievements |
In this project, some theorems on metric-measure spaces which are complete separable metric spaces with Borel probability measures were proved. In particular, one of the main results is that a set of metric-measure spaces is precomapct with respect to the box distance if and only if it is bounded, that is, there exists a metric-measure space which dominates any element in the set with respect to the Lipschitz order as was sketched by M. Gromov (1999). Moreover, several propositions which will be useful in the study of the geometry of metric-measure spaces were also proved.
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