arXiv subjects

Jorge Salazar

Publications and source records attributed to Jorge Salazar.

2 recordsLinked to original sources

arXiv2022

On the Behavior of Unbounded Collatz Sequences

The aim of this paper is to show a peculiar behavior of a (hypothetical) Collatz sequence going to infinity. We study the associated Syracusa sequence (the odd elements of the former) and show that the limit set of a conveniently normalized sequence is the whole unit interval. In particular, for any positive integer there is a subsequence whose elements' expansions in base 3 begin (from the left) with the expansion of the given number.

math.NT↗

arXiv2018

Fubini-Tonelli type theorem for non product measures in a product space

I prove a theorem about iterated integrals for non-product measures in a product space. The first task is to show the existence of a family of measures on the second space, indexed by the points on of the first space (outside a negligible set), such that integrating the measures on the index against the first marginal gives back the original measure (see Theorem 2.1). At the end, I give a simple application in Optimal Transport.

math.PR↗