arXiv subjects

Alex Galicki

Publications and source records attributed to Alex Galicki.

3 recordsLinked to original sources

arXiv2015

Randomness and differentiability in higher dimensions

We present two theorems concerned with algorithmic randomness and differentiability of functions of several variables. Firstly, we prove an effective form of the Rademacher's Theorem: we show that computable randomness implies differentiability of computable Lipschitz functions of several variables. Secondly, we show that weak 2-randomness is equivalent to differentiability of computable a.e. differentiable functions of several variables.

math.LO↗

arXiv2015

Computable randomness and monotonicity

We show that $z\in\R^n$ is computably random if and only if every computable monotone function on $\R^n$ is differentiable at $z$.

math.LO↗

arXiv2013

Aspects of Classical Descriptive Set Theory

This report consists of two parts. The first part is a brief exposition of classical descriptive set theory. This part introduces some fundamental concepts, motivations and results from the classical theory and ends with a section on the important result of Addison that established the correspondence between classical and effective notions. The second part is about invariant descriptive set theory. It consists of a brief introduction to notions relevant to this branch of descriptive set theory and then describes in details some of the relatively recent results concerning equivalence relations between Polish metric spaces.

math.LO↗