Computable measures in computable analysis

News
20 Dec 2012, the slides were uploaded.

Title
Computable measures in computable analysis

Type
Talk
JAIST 20 Dec 2012

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Slides

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Van Lambalgen’s Theorem and Radon-Nikodym derivative

News
26 Oct 2012, the slides were uploaded.

Title
Van Lambalgen’s Theorem and Radon-Nikodym derivative

Type
Young Logician’s Gathering in Japan
23-25 Nov 2012
Nara Seisyounen Kaikan

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Slides

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The law of the iterated logarithm in game-theoretic probability

News
15 Nov 2012, the revised slides were uploaded.
26 Oct 2012, the slides were uploaded.

Title
The law of the iterated logarithm in game-theoretic probability

Type
Fourth Workshop on Game-Theoretic Probability and Related Topics
12-14 Nov 2012
The University of Tokyo

Abstract
The Kolmogorov law of the iterated logarithm (LIL) (1929) provides the exact speed of the convergence of the sum of independent ran- dom variables under a condition. Subsequently, Hartman and Wintner (1941) showed that, in the case of i.i.d. random variables, the existence of a second moment is sufficient for the LIL. Shafer and Vovk (2001)
studied the Kolmogorov LIL in game-theoretic probability and asked the treatment of the Hartman and Winter LIL in game-theoretic prob- ability.
I present a new sufficient condition for the LIL in game-theoretic probability, which has a similar form to the Hartman and Winter LIL. The main idea is to add a little stronger hedges. This is the joint work with Akimich Takemura.

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An introduction to algorithmic randomness

News
15 Nov 2012, the revised slides were uploaded.
26 Oct 2012, the slides were uploaded.

Title
An introduction to algorithmic randomness

Type
Fourth Workshop on Game-Theoretic Probability and Related Topics
12-14 Nov 2012
The University of Tokyo

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Slides

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Where is randomness?

News
2 Oct 2012, the slides were uploaded.

Title
Where is randomness?

Type
Talk at Math Lectures
13 Oct 2012
Kyoto University

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Slides

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Natural properties that a randomness notion should have

News
21 Sep 2012, presented and the final slides were uploaded.
16 Sep 2012, the slides were uploaded.

Title
Natural properties that a randomness notion should have

Type
Talk at
The Mathematical Society of Japan
18-21 Sep 2012
Kyushu University

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Abstract
s-mathsoc

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On the notion of randomness

News
20 Sep 2012, updated the slide and uploaded the lecture note.

Title
On the notion of randomness

Type
Talk at
Summer school of foundations of mathematics
4-7 Sep 2012
Tokyo Institute of Technology

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Slide1 (in Japanese)
Slide2 (in Japanese)
Lecture Note

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An introduction to game-theoretic probability

Title
An introduction to game-theoretic probability

Type
Talk at
SLACS 2012
15-16 Sep, 2012
Kyoto Sangyo University

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Slide

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Schnorr triviality and being a basis for tt-Schnorr randomness

Title
Schnorr triviality and being a basis for tt-Schnorr randomness

Type
Talk at
PROOF THEORY AND COMPLEXITY 2012
12-14 Sep, 2012
Research Institute for Mathematical Sciences,
Kyoto University

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Preliminary report
Slide

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On the effectivization of Lusin’s theorem

Title
On the effectivization of Lusin’s theorem

Type
LA symposium 2012

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Summary in Japanese
Slide

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