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math.LO2015★ 1 cited
Computable randomness and monotonicity
Alex Galicki
We show that is computably random if and only if every computable monotone function on is differentiable at .
math.LO2014★ 1 cited
Randomness and differentiability in higher dimensions
Alex Galicki, Daniel Turetsky
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 Theor…
math.LO2013★ 1 cited
Aspects of Classical Descriptive Set Theory
Alex Galicki
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…