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# Tag Archives: Upper density

## Weighted densities with multiplicative structure

The upper density of a set , defined by provides a useful way to measure subsets of . For instance, whenever , contains arbitrarily long arithmetic progressions, this is Szemerédi’s theorem. A fundamental property of the upper density is that … Continue reading

Posted in Combinatorics, Number Theory, Tool
Tagged erdos, multiplicative structure, Upper density, weighted densities
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## Additive vs multiplicative densities

It is basic fact of measure theory that there is no uniform measure on a countable set such as the set of all natural numbers. However, there are many ways to measure size of subsets of . For instance, the … Continue reading

Posted in Combinatorics
Tagged addition and multiplication, Banach density, folner sequences, natural density, Upper density
1 Comment