Construction of computable measure theory

2017 Fiscal Year Final Research Report

• Project/Area Number: 26870143
• Research Category: Grant-in-Aid for Young Scientists (B)
• Allocation Type: Multi-year Fund
• Research Field: Theory of informatics; Foundations of mathematics/Applied mathematics
• Research Institution: Meiji University
• Principal Investigator: Miyabe Kenshi 明治大学, 理工学部, 専任准教授 (00583866)
• Project Period (FY): 2014-04-01 – 2018-03-31
• Keywords: 計算可能測度論 / Schnorrランダム性 / 密度ランダム性

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.

Free Research Field

計算論