# characteristic function

Definition from Wiktionary, the free dictionary

## Contents

## English[edit]

### Noun[edit]

**characteristic function** (*plural* **characteristic functions**)

- (analysis) A function which is equal to 1 for all points in its domain which belong to a given set, and is equal to 0 for all points in the domain which do not belong to that given set.
- (mathematics, probability theory) A complex function completely defining the probability distribution of a real-valued random variable

#### Usage notes[edit]

- The characteristic function of a set
*A*is often represented as χ_{A}.

#### Synonyms[edit]

- (function equal to 1 on elements of a given set): indicator function

#### Hypernyms[edit]

#### Translations[edit]

function equal to one on elements of a given set —

*see*indicator functiona complex function completely defining a probability distribution