= Monotonicity of a measure
{title2=$A\subseteq B\ \Longrightarrow\ \mu(A)\leq\mu(B)$}
For <measurable sets> $A\subseteq B$, the <disjoint union> $B=A\sqcup(B\setminus A)$ and <finite additivity> give $\mu(B)=\mu(A)+\mu(B\setminus A)\geq\mu(A)$. This uses nonnegativity and is valid with infinite values; it does not subtract infinities. <Monotonicity of a measure> implies that increasing <measurable sets> have nondecreasing <measures>, but the equality of their <limit> with the <measure> of their <union> uses the stronger axiom of <countable additivity>.
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