Strong laws of large numbers for lightly trimmed sums of generalized Oppenheim expansions

Abstract

In the framework of generalized Oppenheim expansions we prove strong law of large numbers for lightly trimmed sums. In the first part of this work we identify a particular class of expansions for which we provide a convergence result assuming that only the largest summand is deleted from the sum; this result generalizes a strong law recently proven for the Luroth case. In the second part we drop any assumptions concerning the structure of the Oppenheim expansions and we prove a result concerning trimmed sums when at least two summands are trimmed; then we derive a corollary for the case in which only the largest summand is deleted from the sum.