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Suppose $T$ is a well-ordered set with minimal value $0$. Let $\lbrace X_t \mid t\in T\rbrace$ be a stochastic process defined on a probability space $(\Omega,\mathcal{F},P)$ and $\lbrace \mathcal{F}_t\rbrace$ a filtration (an increasing sequence of sigma subalgebras of $\mathcal{F}$). Then the process $\lbrace X_t\rbrace$ is said to be \emph{adapted to} the filtration $\lbrace \mathcal{F}_t\rbrace$ if for each $t$, $X_t$ is \PMlinkname{$\mathcal{F}_t$-measurable}{MathcalFMeasurableFunction}:
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Suppose $T$ is a well-ordered set with minimal value $0$. Let $\lbrace f_t \mid t\in T\rbrace$ be a stochastic process defined on a probability space $(\Omega,\mathcal{F},P)$ and $\lbrace \mathcal{F}_t\rbrace$ a filtration (an increasing sequence of sigma subalgebras of $\mathcal{F}$). Then the process $\lbrace f_t\rbrace$ is said to be \emph{adapted to} the filtration $\lbrace \mathcal{F}_t\rbrace$ if for each $t$, $f_t$ is \PMlinkname{$\mathcal{F}_t$-measurable}{MathcalFMeasurableFunction}:
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