  The purpose of this note is to use the results and methods of our previous
work with Bourgain to obtain control and observability by rough functions and
sets on rectangular 2-tori. We show that any Lebesgue measurable set of
positive measure can be used for observability for the Schroedinger equation.
This leads to controllability with rough localization and control functions.
  For non-empty open sets this follows from the results of Haraux '89 and
Jaffard '89 while for square tori and sufficiently long times this can be
deduced from the results of Jakobson '97.
