**News**

23 Feb 2013, the slides were uploaded.

**Title**

Things to do in and with algorithmic randomness

**Type**

Talk

Sendai Logic School 2013

http://sendailogic.math.tohoku.ac.jp/SLS/

Sendai, 22 Feb 2013

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# Month: February 2013

## Things to do in and with algorithmic randomness

## ￼Computably measurable sets and computably measurable functions in terms of algorithmic randomness

## Van Lambalgen’s Theorem for uniformly relative Schnorr and computable randomness

宮部賢志（ミヤベケンシ）

**News**

23 Feb 2013, the slides were uploaded.

**Title**

Things to do in and with algorithmic randomness

**Type**

Talk

Sendai Logic School 2013

http://sendailogic.math.tohoku.ac.jp/SLS/

Sendai, 22 Feb 2013

**Download**

Slide

**News**

20 Feb 2013, the slides were uploaded.

**Title**

Computably measurable sets and computably measurable functions in terms of algorithmic randomness

**Type**

Talk

Computability Theory and Foundations of Mathematics

http://sendailogic.math.tohoku.ac.jp/CTFM/

Tokyo Tech, 20 Feb 2013

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slide

**News**

Feb 2013, accepted

26 Sep 2012, uploaded to arXiv

Aug 2012, submitted

**Title**

Van Lambalgen’s Theorem for uniformly relative Schnorr and computable randomness

(with Jason Rute)

**Type**

Full paper

**Journal**

Proceedings of the Twelfth Asian Logic Conference, World Scientific, 251-270

**Abstract**

We correct Miyabe’s proof of van Lambalgen’s Theorem for truth-table Schnorr randomness (which we will call uniformly rela- tive Schnorr randomness). An immediate corollary is one direction of van Lambalgen’s theorem for Schnorr randomness. It has been claimed in the literature that this corollary (and the analogous result for com- putable randomness) is a “straightforward modification of the proof of van Lambalgen’s Theorem.” This is not so, and we point out why. We also point out an error in Miyabe’s proof of van Lambalgen’s Theorem for truth-table reducible randomness (which we will call uniformly rel- ative computable randomness). While we do not fix the error, we do prove a weaker version of van Lambalgen’s Theorem where each half is computably random uniformly relative to the other.

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