Measures (measure theory)

function assigning numbers to some subsets of a set, which could be seen as a generalization of length, area, volume and integral

extension of the concept of area for an arbitrary dimension

measure that assigns to any subset of the measure space its cardinality as an extended real number

left-invariant (or right-invariant) measure on locally compact topological group

Mathematical function

an extension of the notion of size (length, area, volume) to shapes more complicated than, for example, a triangle, disk, or parallelepiped

measure that is 1 if and only if a specified element is in the set

measure defined on all open sets of a topological space

measure on the σ-algebra of Borel sets of a Hausdorff topological space X that is finite on all compact sets, outer regular on all Borel sets, and inner regular on open sets

fractal measurement

construction in measure theory

generalized notion of measure in mathematics

measure of total value one, generalizing probability distributions

mathematical operator-valued measure of interest in quantum mechanics and functional analysis

measure with complex values

measure space where every subset of a set with null measure is measurable (and has null measure)

mathematical measure

borel measure which is inner and outer regular

generalization of finite measure to Banach spaces

measure or probability distribution whose support has zero Lebesgue (or other) measure

given a Borel measure, the set of those points whose neighbourhoods always have positive measure

measure in which every set contains a neighborhood of finite measure

concept in measure theory

In mathematics, a pre-measure is a set function that is, in some sense, a precursor to a bona fide measure on a given space. Indeed, one of the fundamental theorems in measure theory states that a pre-measure can be extended to a measure.

A measure on one measurable space defined from another using a measurable function.

Measure in measure theory

type of measure on Euclidean spaces

function whose domain is a collection of sets

borel measure which its value on a borel set is determined as the infimum of the measure of its open superset

concept in mathematics

measure that always takes on finite values