finished integrals for real numbers
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@ -609,7 +609,7 @@ All functions from now on will be considered measurable.
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We use $\int_A g \dd\mu$ even if $g$ isn't defined outside of $A$.
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Integrals are independent from the behavior on null sets, so
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\[
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\int_0^1 \rec{x} \dd x = 0
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\int_{-1}^1 \rec{x} \dd x = 0
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\]
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is perfectly fine, even though the integrand is not defined for $x = 0$.
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\end{rem}
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