Schnirelmann density

Let A be a subset of , and let A(n) be number of elements of A in [1,n]. of A is


has the following properties:

  1. 1.

    A(n)nσA for all n.

  2. 2.

    σA=1 if and only if A

  3. 3.

    if 1 does not belong to A, then σA=0.

Schnirelmann proved that if 0AB then


and also if σA+σB1, then σ(A+B)=1. From these he deduced that if σA>0 then A is an additive basis.

Title Schnirelmann densityMathworldPlanetmath
Canonical name SchnirelmannDensity
Date of creation 2013-03-22 13:19:36
Last modified on 2013-03-22 13:19:36
Owner bbukh (348)
Last modified by bbukh (348)
Numerical id 9
Author bbukh (348)
Entry type Definition
Classification msc 11B13
Classification msc 11B05
Synonym Shnirel’man density
Synonym Shnirelman density
Related topic Basis2
Related topic EssentialComponent
Related topic MannsTheorem