Generalised Egorov’s Statement for ideals

Tomasz Weiss has proven that the statement obtained from the
classic Egorov's Theorem by dropping the measurability assumption (so
called generalised Egorov's statement) is independent from ZFC (we
restrict our attention to real functions). We study this statement for
different types of convergence with respect to ideals for some classes
of ideals on the set of natural numbers.