Lower Banach Density

The lower Banach density of a set of integers is

$d_*(A)=lim_(d->infty)inf_(n in Z)(|A intersection {n+1,...,n+d}|)/d.$

It is related to the upper Banach density by

$d_*(A)=1-d^*(Z\A).$

The Banach density of exists when its lower Banach density and upper Banach density are equal.

See also

Banach Density, Natural Density, Upper Banach Density

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References

Richard, C. and Schumacher, C. "On Sampling and Interpolation by Model Sets." J. Fourier Anal. Appl. 26, #39, 2020. https://doi.org/10.1007/s00041-020-09742-w.

Cite this as:

Weisstein, Eric W. "Lower Banach Density." From MathWorld--A Wolfram Resource. https://mathworld.wolfram.com/LowerBanachDensity.html

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