Added notation for space of measurable functions.
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\section{Convergence in Measure}
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\label{section:convergence-in-measure}
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\begin{definition}[In Measure]
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\label{definition:in-measure}
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Let $(X, \cm, \mu)$ be a measure space, $(Y, d)$ be a metric space, then the uniform
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\end{definition}
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\begin{definition}[Convergence in Measure]
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\label{definition:convergence-in-measure}
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Let $(X, \cm, \mu)$ be a measure space, $(Y, d)$ be a metric space, and $\fF$ be a filter of $(\cm, \cb_Y)$-measurable functions, and $f$ be a $(\cm, \cb_Y)$-measurable function, then $\fF \to f$ \textbf{in measure} if for each $\eps > 0$,
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