On topological properties of the set of maldistributed sequences

The real sequence (x_n) is maldistributed if for any non-empty interval I, the set {n ∈𝕅 : x_n ∈I} has upper asymptotic density 1. The main result of this note is that the set of all maldistributed real sequences is a residual set in the set of all real sequences (i.e., the maldistribution is a typical property in the sense of Baire categories). We also generalize this result.