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What does it mean when we say that a functionvanishes outside a set of finite measure? As in the definition of the integral as a prelude to the Lebesgue integral in Royden's Real Analysis, 3rd ed. (p. 77). It said:

If [tex]\phi[/tex] vanishes outside a set of finite measure, we define the integral of [tex]\phi[/tex] by

[tex]\int{\phi(x)dx} = \sum^{n}_{i=1}{{a_i}{mA_i}}[/tex]

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# Meaning of vanishes outside a set of finite measure

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