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...

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...

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...

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...

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...

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...

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...

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...

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...

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...

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

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...

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

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...

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

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...

computational chemistry, a basis set is a set of functions (called basis functions) that is used to represent the electronic wave function in the Hartree–Fock method...

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...

variables, functions, or even other sets. A set may also be called a collection or family, especially when its elements are themselves sets; this may avoid...

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...

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...

codomain of a function, the function does not change as a set since by definition it is just a set of ordered pairs. That is, a function does not determine...

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

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

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

§ Limitations below. The set of primitive recursive functions is known as PR in computational complexity theory. A primitive recursive function takes a fixed number...

analytic function is a function that is locally given by a convergent power series. There exist both real analytic functions and complex analytic functions. Functions...