(mathematical analysis) A subset of a given measurable space which is a member of the σ-algebra of that space.

(mathematical analysis, of a function) Such that the inverse image of any open set in its codomain is a Borel set of its domain.

(mathematical analysis) A function whose domain is a σ-algebra, whose codomain is [0,∞], and which is countably additive.

(mathematical analysis) A function whose domain is a σ-algebra, whose codomain is the set of complex numbers, and which is countably additive.

(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).