Let a = {A(n)}(n >= 1) be a sequence of left-open and right-closed intervals which partition (0,1]. The alpha-Luroth transformation L-alpha is defined as an infinite piecewise linear map which maps A(n) linearly onto (0,1] for every n >= 1. Then every point x is an element of (0,1] is attached with a finite or infinite integer sequence {l(n)}(n >= 1) by looking at the coding of its trajectory. In this note, we consider the size of the recurrent set in such a system. More precisely, let x(0) is an element of (0,1] with an infinite alpha-Luroth expansion, and {t(n)}(n >= 1) an arbitrary non-decr...
