P. Leonetti

activity

20122026

most citedOn the notions of upper and lower density

20 citations · 109 across the 55 of their papers we have counts for

collaborators

Showing 2017Show all

8 papers · 1 filter

math.FA2017

Duality between Measure and Category of Almost All Subsequences of a Given Sequence

Paolo Leonetti, Harry Miller, Leila Miller-Van Wieren

Let $S$ be the set of subsequences $(x_{n_{k}})$ of a given real sequence $(x_{n})$ which preserve the set of statistical cluster points. It has been recently shown that $S$ is a set o…

math.NT2017★ 1 cited

A note on primes in certain residue classes

Paolo Leonetti, Carlo Sanna

Given positive integers $a_{1}, \dots, a_{k}$ , we prove that the set of primes $p$ such that $p \neq \equiv 1 mod a_{i}$ for $i = 1, \dots, k$ admits asymptotic density relative to the set…

math.FA2017

On the Relationship between Ideal Cluster Points and Ideal Limit Points

Marek Balcerzak, Paolo Leonetti

Let $X$ be a first countable space which admits a non-trivial convergent sequence and let $I$ be an analytic P-ideal. First, it is shown that the sets of $I$ -li…

math.CA2017

A Characterization of Convex Functions

Paolo Leonetti

Let $D$ be a convex subset of a real vector space. It is shown that a radially lower semicontinuous function $f : D \to R \cup {+ \infty}$ is convex if and only if for all $…

math.CA2017

Invariance of Ideal Limit Points

Paolo Leonetti

Let $I$ be an analytic P-ideal [respectively, a summable ideal] on the positive integers and let $(x_{n})$ be a sequence taking values in a metric space $X$ . First, it is s…

math.CA2017

Characterizations of Ideal Cluster Points

Paolo Leonetti, Fabio Maccheroni

Given an ideal $I$ on $ω$ , we prove that a sequence in a topological space $X$ is $I$ -convergent if and only if there exists a ``big'' $I$ -convergent…