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indicator function : ウィキペディア英語版
indicator function

In mathematics, an indicator function or a characteristic function is a function defined on a set ''X'' that indicates membership of an element in a subset ''A'' of ''X'', having the value 1 for all elements of ''A'' and the value 0 for all elements of ''X'' not in ''A''. It is usually denoted by a bold or blackboard bold 1 symbol with a subscript describing the event of inclusion.
==Definition==
The indicator function of a subset ''A'' of a set ''X'' is a function
:\mathbf_A \colon X \to \ \,
defined as
:\mathbf_A(x) :=
\begin
1 &\text x \in A, \\
0 &\text x \notin A.
\end

The Iverson bracket allows the equivalent notation, (A ), to be used instead of \mathbf_A(x).
The function \mathbf_A is sometimes denoted I_A, \chi_A or even just A. (The Greek letter \chi appears because it is the initial letter of the Greek word ''characteristic''.)

抄文引用元・出典: フリー百科事典『 ウィキペディア(Wikipedia)
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