Search results
Results from the WOW.Com Content Network
The indicator function of A is the Iverson bracket of the property of belonging to A; that is, = [ ] . For example, the Dirichlet function is the indicator function of the rational numbers as a subset of the real numbers.
Such indicators have some special properties. For example, the following statements are all true for an indicator function that is trigonometrically convex at least on an interval (,): [1]: 55–57 [2]: 54–61
In mathematics, the Dirichlet function [1] [2] is the indicator function ... The Dirichlet function is an archetypal example of the Blumberg theorem.
To put it more simply, the indicator vector of T is a vector with one element for each element in S, with that element being one if the corresponding element of S is in T, and zero if it is not. [1] [2] [3] An indicator vector is a special (countable) case of an indicator function.
A simple function can be written in different ways as a linear combination of indicator functions, but the integral will be the same by the additivity of measures. Some care is needed when defining the integral of a real-valued simple function, to avoid the undefined expression ∞ − ∞ : one assumes that the representation
Indicator function: maps x to either 1 or 0, depending on whether or not x belongs to some subset. Step function: A finite linear combination of indicator functions of half-open intervals. Heaviside step function: 0 for negative arguments and 1 for positive arguments. The integral of the Dirac delta function. Sawtooth wave; Square wave ...
One example of such a function is the indicator function of the rational numbers, also known as the Dirichlet function. This function is denoted as 1 Q {\displaystyle \mathbf {1} _{\mathbb {Q} }} and has domain and codomain both equal to the real numbers .
A Dirac measure is a measure δ x on a set X (with any σ-algebra of subsets of X) defined for a given x ∈ X and any (measurable) set A ⊆ X by = = {,;,.where 1 A is the indicator function of A.