mathematics, a continuous function is a function such that a small variation of the argument induces a small variation of the value of the function. This implies...

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)...

⊆ absolutely continuous ⊆ bounded variation ⊆ differentiable almost everywhere. A continuous function fails to be absolutely continuous if it fails to...

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...

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

the Weierstrass function, named after its discoverer, Karl Weierstrass, is an example of a real-valued function that is continuous everywhere but differentiable...

a quasi-continuous function is similar to, but weaker than, the notion of a continuous function. All continuous functions are quasi-continuous but the...

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

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

In probability theory and statistics, a probability distribution is a function that gives the probabilities of occurrence of possible events for an experiment...

particularly in game theory and mathematical economics, a function is graph continuous if its graph—the set of all input-output pairs—is a closed set in the product...

or bicontinuous function, is a bijective and continuous function between topological spaces that has a continuous inverse function. Homeomorphisms are...

the 19th century in terms of set theory, and this greatly increased the possible applications of the concept. A function is often denoted by a letter...

that every continuous function defined on a closed interval [a, b] can be uniformly approximated as closely as desired by a polynomial function. Because...

In mathematical analysis, a family of functions is equicontinuous if all the functions are continuous and they have equal variation over a given neighbourhood...

 178. Sofronidis, Nikolaos Efstathiou (2005). "The set of continuous piecewise differentiable functions". Real Analysis Exchange. 31 (1): 13–22. doi:10.14321/realanalexch...

Lipschitz, is a strong form of uniform continuity for functions. Intuitively, a Lipschitz continuous function is limited in how fast it can change: there exists...

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

the function, to subsets of another set. Set-valued functions are used in a variety of mathematical fields, including optimization, control theory and...

instantaneous impulses. It is called the delta function because it is a continuous analogue of the Kronecker delta function, which is usually defined on a discrete...

In probability theory and statistics, the cumulative distribution function (CDF) of a real-valued random variable X {\displaystyle X} , or just distribution...

analysis and measure theory, an approximately continuous function is a concept that generalizes the notion of continuous functions by replacing the ordinary...

In mathematics, a real function f {\displaystyle f} of real numbers is said to be uniformly continuous if there is a positive real number δ {\displaystyle...

\mathbb {R} } , and upper semi-continuous if − f {\displaystyle -f} is lower semi-continuous. A function is continuous if and only if it is both upper...

than continuous maps. Recall that, by definition, a function f : X → Y {\displaystyle f:X\to Y} is continuous if the preimage of every open set of Y {\displaystyle...

analysis and related areas of mathematics, a continuous linear operator or continuous linear mapping is a continuous linear transformation between topological...

theory, a map may refer to a morphism. The term transformation can be used interchangeably, but transformation often refers to a function from a set to...

interpretations, probability theory treats the concept in a rigorous mathematical manner by expressing it through a set of axioms. Typically these axioms...

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...

identity function f on X is often denoted by idX. In set theory, where a function is defined as a particular kind of binary relation, the identity function is...