Conditional expectation limit to $-\infty$

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In my lecture notes, I came across the following:

Let $E(Y|X=x) = \mu(x)$ be continuously differentiable. Then by the fundamental theorem of calculus, we have $\mu(x) = \lim_{t \rightarrow -\infty} \mu(t) + \int_{-\infty}^{x} \mu'(t) dt$.

Apparently the first term $\lim_{t \rightarrow -\infty} \mu(t) = 0$, why is this?