The Index of a Point Lattice in a Set Original Research Article

Let L subset of Rn be an r-dimensional point lattice, 1 ≤ r ≤ n, and B subset of Rn be a measurable set In the paper the index [B : L] of L in B is introduced as the measure (or cardinality if it is finite) of the set of different residue classes module (L) intersecting B. Different descriptions of [B : L] are given, basic properties of [B : L] are studied, lower and upper estimations of [B : L] are proved in the paper.