Set function information

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...

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...

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

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...

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...

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, 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...

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

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...

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...

bijection, bijective function, or one-to-one correspondence between two mathematical sets is a function such that each element of the second set (the codomain)...

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

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...

codomain 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...

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...

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

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...

In mathematics, a level set of a real-valued function f of n real variables is a set where the function takes on a given constant value c, that is: L...

quasiconvex function is a real-valued function defined on an interval or on a convex subset of a real vector space such that the inverse image of any set of the...

codomain and the image of a function are the same set; such a function is called surjective or onto. For any non-surjective function f : X → Y , {\displaystyle...

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

In mathematics, the graph of a function f {\displaystyle f} is the set of ordered pairs ( x , y ) {\displaystyle (x,y)} , where f ( x ) = y . {\displaystyle...