The same as a degenerate distribution.
In the West it is unusual to identify the notions of a degenerate distribution and an improper distribution. For the first see Degenerate distribution; the latter is defined as a measure $\mu$ on the Borel sets of $\mathbf R$ such that $\mu(\mathbf R)<1$.
Improper distribution. Encyclopedia of Mathematics. URL: http://encyclopediaofmath.org/index.php?title=Improper_distribution&oldid=31582