The index of a point lattice in a set
Let \(B\subset \mathbb{R}^n\) be a measurable set and for \(r\in [1, n]\) let \(L\subset \mathbb{R}^n\) be an \(r\)-dimensional point lattice. Then the author introduces the index \([B: L]\) of \(L\) in \(B\) as the measure of the set of different residue classes modulo \((L)\) intersecting \(B\). The author gives some descriptions of \([B: L]\) and some of its basic properties. Finally upper and lower bounds for \([B: L]\) are given.
scientific article; zbMATH DE number 809121