Search results
Results From The WOW.Com Content Network
In mathematics, a set A is a subset of a set B if all elements of A are also elements of B; B is then a superset of A. It is possible for A and B to be equal; if they are unequal, then A is a proper subset of B. The relationship of one set being a subset of another is called inclusion (or sometimes containment).
A three-dimensional plot of an indicator function, shown over a square two-dimensional domain (set X): the "raised" portion overlays those two-dimensional points which are members of the "indicated" subset (A). In mathematics, an indicator function or a characteristic function of a subset of a set is a function that maps elements of the subset ...
In mathematics, especially measure theory, a set function is a function whose domain is a family of subsets of some given set and that (usually) takes its values in the extended real number line {}, which consists of the real numbers and .
Also, in probability, σ-algebras are pivotal in the definition of conditional expectation. In statistics, (sub) σ-algebras are needed for the formal mathematical definition of a sufficient statistic, [3] particularly when the statistic is a function or a random process and the notion of conditional density is not applicable.
In mathematics, the empty set or void set is the unique set having no elements; its size or cardinality (count of elements in a set) is zero. [1] Some axiomatic set theories ensure that the empty set exists by including an axiom of empty set , while in other theories, its existence can be deduced.
In mathematics, the support of a real-valued function is the subset of the function domain of elements that are not mapped to zero. If the domain of f {\displaystyle f} is a topological space , then the support of f {\displaystyle f} is instead defined as the smallest closed set containing all points not mapped to zero.
However, the definition of maximal and minimal elements is more general. In particular, a set can have many maximal and minimal elements, whereas infima and suprema are unique. Whereas maxima and minima must be members of the subset that is under consideration, the infimum and supremum of a subset need not be members of that subset themselves.
The arithmetic mean of a series of values ,, …, is often denoted by placing an "overbar" over the symbol, e.g. ¯, pronounced "bar". Some commonly used symbols for sample statistics are given below: the sample mean ¯,