Midwest Computability Seminar

Part ix

The Midwest Computability Seminar is meeting remotely in the fall of 2020. The recurring Zoom link is:


Meeting ID: 997 5433 2165

Passcode: midwest

Panopto video     YouTube video

This session will be held jointly with the Computability Theory and Applications Online Seminar.

DATE: Tuesday, December 8th, 2020

TIME: 3:00 - 4:00 PM Central

SPEAKER: Linda Westrick - The Pennsylvania State University

Luzin's (N) and randomness reflection

We show that a computable real-valued function f has Luzin's property (N) if and only if it reflects Π11-randomness, if and only if it reflects Δ11-randomness relative to Kleene's O, and if and only if it reflects Kurtz randomness relative to Kleene's O.  Here a function f is said to reflect a randomness notion R if whenever f(x) is R-random, then x is R-random as well.  If additionally f is known to have bounded variation, then we show f has Luzin's (N) if and only if it reflects weak-2-randomness, and if and only if it reflects Kurtz randomness relative to 0'.  This links classical real analysis with algorithmic randomness.  Joint with Arno Pauly and Liang Yu.

Past Sessions

Previous Seminars:

If you haven't been receiving the announcements and would like to be included in the list, send an email to drh@math.uchicago.edu.