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Math Help - Indicator functions

  1. #1
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    Indicator functions

    I don't understand what an indicator function is. The definition says
    I(A) = 1 if x belongs to A, where A subset of S and
    I(A) = 0 if x does not belong to A.

    But I am not clear. Can you give me an example?
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  2. #2
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    Quote Originally Posted by poorna View Post
    I don't understand what an indicator function is. The definition says
    I(A) = 1 if x belongs to A, where A subset of S and
    I(A) = 0 if x does not belong to A.
    Your notation is not usual. Here it is: \chi _A (x) = \left\{ {\begin{array}{ll}<br />
   {1,} & {x \in A}  \\   {0,} & {x \notin A}  \\ \end{array} } \right.

    Consider: X = \left\{ {a,b,c,d,e} \right\},\;A = \left\{ {a,c,e} \right\},\;\& \;B = \left\{ {b,c,d} \right\}\;.
    \begin{gathered}<br />
  \chi _A (a) = 1,\chi _A (b) = 0,\chi _A (c) = 1,\chi _A (d) = 0,\chi _A (e) = 1 \hfill \\<br />
  \chi _B (a) = 0,\chi _B (b) = 1,\chi _B (c) = 1,\chi _B (d) = 1,\chi _B (e) = 0, \hfill \\ <br />
\end{gathered}
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  3. #3
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    Quote Originally Posted by poorna View Post
    I don't understand what an indicator function is. The definition says
    I(A) = 1 if x belongs to A, where A subset of S and
    I(A) = 0 if x does not belong to A.

    But I am not clear. Can you give me an example?
    Let A = \mathbb{Z} and S = \mathbb{R}.

    Then I(A) = 1 if A is an integer number. For all other values I(A) = 0.

    I've attached the graph of this specific indicator function.
    Attached Thumbnails Attached Thumbnails Indicator functions-indicator.png  
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  4. #4
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    thanks!

    I got it, thank you I read somewhere that step functions are sums of indicator functions. Is that right?
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