| Budget Amount *help |
¥3,900,000 (Direct Cost: ¥3,000,000、Indirect Cost: ¥900,000)
Fiscal Year 2017: ¥780,000 (Direct Cost: ¥600,000、Indirect Cost: ¥180,000)
Fiscal Year 2016: ¥780,000 (Direct Cost: ¥600,000、Indirect Cost: ¥180,000)
Fiscal Year 2015: ¥780,000 (Direct Cost: ¥600,000、Indirect Cost: ¥180,000)
Fiscal Year 2014: ¥1,560,000 (Direct Cost: ¥1,200,000、Indirect Cost: ¥360,000)
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| Outline of Final Research Achievements |
In this research, we aimed to develop the basis of computable measure theory. As products, we proposed some new measures of randomness and proved its nice properties. In concrete, we prove some nice properties of Schnorr randomness version of LR-reducibility, that naturally comes from uniform relativization of Schnorr randomness as LR-reducibility with Martin-Lof randomness does.
We also proposed density randomness as a new randomness notions, which appears in the study of computability of Lebesgue density theorem. Density randomness is closely related with the convergence of martingales and has many equivalent characterizations. We hope to have many and wide applications of this notion.
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