L^1-computability and weak L^1-computability

L^1-computability and weak L^1-computability

Talk at “Kyoto computable analysis Symposium 2012” on 24-27 Feb 2012.

Computable functions are simple functions and
in Weihrauch approach computable functions are always continuous.
However there are some simple discontinuous functions such as the
floor function.
Therefore we need another mathematical notion to measure simplicity.
One candidate is L^1-computability, which was introduced by Pour-El
and Richard 1989.
In this talk I show you that more effectivised version of L^1-computability
has a strong connection with Schnorr randomness
and that some weaker versions of L^1-computability has connections
with some stronger randomness notions.