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Math Help - Absolute Value Integration

  1. #1
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    Absolute Value Integration

    Show that:

    |f - g| is integrable.
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  2. #2
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    Quote Originally Posted by Coda202 View Post
    Show that:

    |f - g| is integrable.
    Well, it isn't in general! If you forgot to include the hypotheses that f and g are themselves integrable, then you can use the fact that |f- g|= f- g as long as f(x)> g(x) and |f- g|= g- f as long as f(x)< g(x).
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  3. #3
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    Quote Originally Posted by Coda202 View Post
    Show that:

    |f - g| is integrable.
    If h_1,h_2 are integrable then h_1\pm h_2 are integrable.
    And if h_3 is integrable then |h_3| is integrable.

    Therefore, if f,g are integrable then f-g is integrable and that implies |f-g| is integrable.
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