Metric Theorems
Metric theorems describe the behaviour of a parametrised sequence for almost all values of some parameter α: that is, for values of α not lying in some exceptional set of Lebesgue measure zero.
- For any sequence of distinct integers bn, the sequence {bn α} is equidistributed mod 1 for almost all values of α.
- The sequence {αn} is equidistributed mod 1 for almost all values of α > 1.
It is not known whether the sequences {en} or {πn} are equidistributed mod 1. However it is known that the sequence {αn} is not equidistributed mod 1 if α is a PV number.
Read more about this topic: Equidistributed Sequence