## Total-machine reducibility and randomness notions

News
4 Jan 2015, the slide file was uploaded

Title
Total-machine reducibility and randomness notions

slide

## Derandomization in game-theoretic probability

News
13 Nov 2014, the slide file was uploaded

Title
Derandomization in game-theoretic probability

miyabe-gtp2014

## Mathematical Seminar, Oct 2014

An article was published in Mathematical Seminar Oct 2014.

## Betting game and mathematics

News
17 Aug 2014, the slide file was uploaded

Title
Betting game and mathematics

Type
Summer Seminar of Meiji University for high school students

miyabe-summer-seminar-2014

## Derandomization in Game-Theoretic Probability

News
27 Sep 2014, Online
3 Aug 2014, Accepted in SPA
12 Feb 2014. Submitted

Title
Derandomization in Game-Theoretic Probability
(with A. Takemura)

Type
Full paper

Journal
Stochastic Processes and their Applications 125, 39-59, 2015

Abstract
We give a general method for constructing a deterministic strategy
of Reality from a randomized strategy in game-theoretic probability.
The construction can be seen as derandomization in game-theoretic probability.

preprint

## Schnorr randomness versions of K, C, LR, vL-reducibilities

News
19 June 2014, the slide file was uploaded
13 June 2014, the talk was given

Title
Schnorr randomness versions of K, C, LR, vL-reducibilities

miyabe-ccr2014

## Mathematical formulation of “unpredictability” ~Non-use of probabilistic models~

News
13 May 2014, Abstract in Japanese was uploaded

Title
Mathematical formulation of “unpredictability” ~Non-use of probabilistic models~

Type
Seminar Talk

## Algorithmic randomness over general spaces

News
7 May 2014. Published online
Dec 2013. Accepted
May, 2012. Resubmit
Sep, 2011. Resubmitted a revised version
25 May, 2010. Submitted to a Journal

Title
Algorithmic randomness over general spaces

Type
Fullpaper

Journal
Math. Log. Quart. 60, No. 3, 184–204 (2014)
DOI 10.1002/malq.201200051

preprint

Abstract
The study of Martin-Löf randomness on a computable metric space with a computable measure has had much progress recently.
In this paper we study Martin-Löf randomness on a more general space, that is, a computable topological space with a computable measure.
On such a space, Martin-Löf randomness may not be a natural notion because there is not a universal test, and Martin-Löf randomness and complexity randomness (defined in this paper) do not coincide in general. We show that SCT3 is a sufficient condition for the existence and the coincidence and study how much we can weaken the condition.