  We prove that if a Bessel sequence in a Hilbert space, that is indexed by a
countably infinite group in an invariant manner, can be partitioned into
finitely many Riesz basic sequences, then each of the sets in the partition can
be chosen to be syndetic. We then apply this result to prove that if a Fourier
frame for a measurable subset of a higher dimensional cube can be partitioned
into Riesz basic sequences, then each subset can be chosen to be a syndetic
subset of the corresponding higher dimensional integer lattice. Both of these
results follow from a result about syndetic pavings of elements of the von
Neumann algebra of a discrete group.
