On the notions of upper and lower density

DOI10.1017/S0013091519000208zbMath1442.11019arXiv1506.04664WikidataQ127302600 ScholiaQ127302600MaRDI QIDQ5111608

Salvatore Tringali, Paolo Leonetti

Publication date: 27 May 2020

Published in: Proceedings of the Edinburgh Mathematical Society (Search for Journal in Brave)

Full work available at URL: https://arxiv.org/abs/1506.04664

zbMATH Keywords

axiomatizationlogarithmic densityasymptotic (or natural) densityupper and lower densitiesanalytic densityBuck densityPólya densityBanach (or uniform) den- sity

Mathematics Subject Classification ID

Real- or complex-valued set functions (28A10) Functional equations for functions with more general domains and/or ranges (39B52) Density, gaps, topology (11B05) Probability theory on algebraic and topological structures (60B99)

Related Items (18)

Highly sparse sets as additive complements for a prescribed density ⋮ A note on the density of k-free polynomial sets, Haar measure and global fields ⋮ On the density of sumsets ⋮ Turnpike in infinite dimension ⋮ Sumsets with prescribed lower and upper asymptotic densities ⋮ Mathias and silver forcing parametrized by density ⋮ Most numbers are not normal ⋮ Almost all sets of nonnegative integers and their small perturbations are not sumsets ⋮ Combinational proof for a theorem concerning the upper Banach density ⋮ Capacities and Choquet averages of ultrafilters ⋮ Densities on Dedekind domains, completions and Haar measure ⋮ Integrability of sequences ⋮ Additive complements for a given asymptotic density ⋮ Chain recurrence and positive shadowing in linear dynamics ⋮ A generalization of the density zero ideal ⋮ F-hypercyclic operators on Fréchet spaces ⋮ On small sets of integers ⋮ A Characterization of Cesàro Convergence

Cites Work

• Unnamed Item
• Unnamed Item
• Unnamed Item
• Unnamed Item
• Unnamed Item
• Unnamed Item
• Unnamed Item
• Unnamed Item
• Unnamed Item
• Unnamed Item
• Unnamed Item
• Unnamed Item
• Unnamed Item
• Unnamed Item
• Unnamed Item
• Unnamed Item
• Extreme points of the set of density measures
• Upper and lower densities have the strong Darboux property
• Density sets of sets of positive integers
• A note on uniform or Banach density
• Répartition des densites des sous-suites d'une suite d'entiers
• An axiomatic approach to complete patience and time invariance
• Thinnable ideals and invariance of cluster points
• Densities and summability
• Lévy group and density measures
• The primes contain arbitrarily long arithmetic progressions
• A note on extensions of asymptotic density
• Lattice Theory: Foundation
• The Mathematical Coloring Book
• Fine asymptotic densities for sets of natural numbers
• On sets of integers containing k elements in arithmetic progression
• Abstract densities and ideals of sets
• Finitely Additive Measures on N and the Additive Property
• Density and multiplicative structure of sets of integers
• The asymptotic density of sequences
• On Certain Sets of Integers
• Generalized Asymptotic Density
• The Measure Theoretic Approach to Density
• Finitely additive measures on \(\mathbb{N}\)

This page was built for publication: On the notions of upper and lower density