The Khintchin class of an increasing sequence of integers {a_n} is defined to be the class of those Lebesgue-integrable functions f on the circle \mathbb{T} such that the Weyl equidistribution criterion for the sequence {a_n x} holds with f for almost every x. This concept is naturally extended to all compact abelian groups. Khinchin conjectured that for the whole set of integers \mathbb{N}, the Khintchin class includes the space of all bounded measurable functions. But it was refuted by Marstrand (1970). If the Khintchin class of a sequence of integers is equal to L^1(\mathbb{T}), we say that the set is a Khintchin sequence. We try to use the skew product to generate random Khintchin sequences. Open questions will be presented.

230903-scms seminar-fah.pdf