Small subset of the plane which almost contains almost all Borel functions

Janusz Pawlikowski

Vol. 144 (1990), No. 1, 155–160

DOI: 10.2140/pjm.1990.144.155

Abstract

A Borel subset B of the plane is constructed which is small from the Lebesgue measure point of view and large in the sense of the Baire category. All vertical sections of B have measure zero, and for each Borel function f : R → R for all but countably many y the set {x ∈ R : (x,f(x) + y) ∈ B} is comeager.

Mathematical Subject Classification 2000

Primary: 28A05

Secondary: 03E15, 04A15

Milestones

Received: 13 September 1988

Published: 1 July 1990