Mathematics-Online lexicon: Properties of the Multiple Integral

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	Mathematics-Online lexicon:
	Properties of the Multiple Integral

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The following properties hold for integrals:

Linearity: $\quad \int\limits_Vaf+bg=a\int\limits_V f + b \int\limits_V g, \qquad a,b \in \mathbb{R}$
Monotony: $\quad f(x)\leq g(x)$ for all $x\in V \Longrightarrow \int\limits_V f\leq \int\limits_V g$
Additivity: $\quad \int\limits_V f= \int\limits_{V_1} f + \int\limits_{V_2} f ,\quad$ if is the union of the two regions and which are disjoint except possibly at their boundaries.

(Authors: Boßle/Höllig/Streit/Höfert)

automatically generated 8/ 4/2008