(mathematical analysis) A positive measure which, for each subset of a given measure space, assigns a value equal to the number of points in that subset.

plural of measurable set

(mathematical analysis) A measure such that, for every set of measure zero belonging to its domain, all subsets of that set are also assigned measure zero by the given measure.

(mathematical analysis) A measure whose domain is the Borel σ-algebra of a locally compact Hausdorff space.

(mathematical analysis) (of a set in some k-dimensional Euclidean space) That it is an element of the domain of the Lebesgue measure of the ambient Euclidean space.

(mathematical analysis) A unique complete translation-invariant measure for the σ-algebra which contains all k-cells in a given Euclidean space, and which assigns a measure to each k-cell which is equal to that k-cell's volume (as defined in Euclidean geometry: i.e., the volume of the k-cell equals the product of the lengths of its sides).

(mathematics) A mathematical measure on a probability space that can take on values between 0 and 1, with 0 corresponding to the empty set and 1 to the entire space.

plural of measurable function

plural of measurable space

plural of measure space