Giuliano, Rita and Hadjikyriakou, Milto ORCID: 0000-0001-5672-7792 (2023) Strong laws of large numbers for lightly trimmed sums of generalized Oppenheim expansions. (Submitted)
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Official URL: https://doi.org/10.48550/arXiv.2311.02764
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.
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