Density Point

in mathematics. A density point of a set is a point such that the ratio of the measure of the part of the set in the neighborhood to the measure of the neighborhood—the so-called relative measure of a neighborhood of the point—approaches unity as the neighborhood shrinks to the point. In any measurable set, points that are not density points form a set of measure zero. Density points are of interest in the study of the asymptotic or approximative behavior of a function when the function in the neighborhood of a given point is considered not over the entire domain of definition but over a set for which the point is a density point. This is the case, for example, in the study of asymptotic continuity and of the derivative and differential.