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\begin{enumerate}
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\item For each $t \ge 0$, $\bp_t \one = \one$.
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\item For each $t \ge 0$, $\bp_t$ is a positive linear functional.
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\end\{enumerate\}
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\end{enumerate}
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known as the \textbf{semigroup} of $\bracs{P_t|t \ge 0}$.
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\end{definition}
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