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...

a function from a set X to a set Y assigns to each element of X exactly one element of Y. The set X is called the domain of the function and the set Y...

mathematics, a superadditive set function is a set function whose value when applied to the union of two disjoint sets is greater than or equal to the...

submodular set function (also known as a submodular function) is a set function that, informally, describes the relationship between a set of inputs and...

subadditive set function is a set function whose value, informally, has the property that the value of function on the union of two sets is at most the...

an additive set function is a function μ \mu mapping sets to numbers, with the property that its value on a union of two disjoint sets equals the sum...

In mathematics, a monotonic function (or monotone function) is a function between ordered sets that preserves or reverses the given order. This concept...

In mathematics, the domain of a function is the set of inputs accepted by the function. It is sometimes denoted by dom ⁡ ( f ) {\displaystyle \operatorname...

the set of all elements of X {\displaystyle X} that map to a member of B . {\displaystyle B.} The image of the function f {\displaystyle f} is the set of...

A set-valued function, also called a correspondence or set-valued relation, is a mathematical function that maps elements from one set, the domain of the...

primitive recursive set functions or primitive recursive ordinal functions are analogs of primitive recursive functions, defined for sets or ordinals rather...

set and the Fatou set are two complementary sets (Julia "laces" and Fatou "dusts") defined from a function. Informally, the Fatou set of the function...

hypothesis on the codomain of the function, a level set of a function f {\displaystyle f} is the zero set of the function f − c {\displaystyle f-c} for some...

In mathematics, a function space is a set of functions between two fixed sets. Often, the domain and/or codomain will have additional structure which...

In mathematics, an indicator function or a characteristic function of a subset of a set is a function that maps elements of the subset to one, and all...

counter-domain, or set of destination of a function is a set into which all of the output of the function is constrained to fall. It is the set Y in the notation...

transformation, transform, or self-map is a function f, usually with some geometrical underpinning, that maps a set X to itself, i.e. f: X → X. Examples include...

In mathematics, a partial function f from a set X to a set Y is a function from a subset S of X (possibly the whole X itself) to Y. The subset S, that...

well-behaved boundary. Below it, the red surface is the graph of a level set function φ {\displaystyle \varphi } determining this shape, and the flat blue...

In set theory, a continuous function is a sequence of ordinals such that the values assumed at limit stages are the limits (limit suprema and limit infima)...

In mathematics, the Cantor function is an example of a function that is continuous, but not absolutely continuous. It is a notorious counterexample in...

mathematics, and in particular measure theory, a measurable function is a function between the underlying sets of two measurable spaces that preserves the structure...

function is a function on a lattice that, informally, has the property of being characterized by "increasing differences." Seen from the point of set...

a function is convex if its epigraph (the set of points on or above the graph of the function) is a convex set. In simple terms, a convex function graph...

a set f ⊂ X × Y {\displaystyle f\subset X\times Y} involving unbounded collections constitute a (mathematical, and so always meaning total) function. This...

surjective function (also known as surjection, or onto function /ˈɒn.tuː/) is a function f such that, for every element y of the function's codomain, there...

It is a set-valued function with additional properties depending on context; some authors do not distinguish between set-valued functions and multifunctions...

Computable functions are the basic objects of study in computability theory. Informally, a function is computable if there is an algorithm that computes...

In mathematics, an injective function (also known as injection, or one-to-one function ) is a function f that maps distinct elements of its domain to...

a probability density function (PDF), density function, or density of an absolutely continuous random variable, is a function whose value at any given...