Pure Math Colloquium

Linda Westrick, Pennsylvania State University

"Luzin's (N) and randomness reflection"

A function f:R->R has Luzin's property (N) if f(A) has Lebesgue measure 0 for every set A of Lebesgue measure 0.  We give a new characterization of this old property in terms of higher algorithmic randomness.  A computable f has Luzin's (N) if and only if it satisfies the following pointwise condition: for all reals x, if f(x) is Pi^1_1-random, then so is x.  Here an individual real x is called Pi^1_1-random if it is not contained in any computably describable co-analytic set of measure 0.  Joint work with Arno PAULY and YU Liang.

Zoom meeting: https://zoom.us/j/93240216981?pwd=aE0vbktRV1NvMTFzbFVaalVpb1pCdz09