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Prof. Dr. Linda Westrick (Pennsylvania State University)

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 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-randomthen 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. All these notions will be defined in the talk without assuming any prior knowledge of them. Joint work with Arno PAULY and YU Liang.

If you wish to attend one (or more) of the talks please send to request for the zoom link to anapde_mathematik.tu-darmstadt.de (please replace  _ by @ ). Please include in your mail your full name, status (teacher, professor, student,...) and institution.

Wenn Sie als Zuhörer*in an den Kolloquien teilnehmen möchten, schicken Sie bitte eine Anfrage per Mail an anapde_mathematik.tu-darmstadt.de (ersetzen Sie dabei bitte _ durch @ ). Ihre Mail sollte Ihren vollständigen Namen, Ihren Status (Lehrer*in, Professor*in, Student*in, Doktorand*in , ...) und Ihre Institution enthalten.


08. Dezember 2021, 17:15-19:00




FB Mathematik, AG Numerik und wissenschaftliches Rechnen


Prof. Dr. Jan Giesselmann




Mathematisches Kolloquium, Mathematik, Numerik