  Given a sequence of Borel probability measures on a Hausdorff space which
satisfy a large deviation principle, we consider the corresponding sequence of
measures formed by conditioning on a set $B$. If the large deviation rate
function $I$ is good and effectively continuous and the conditioning set has
the property that (1) $\overline{B^\circ} = \overline{B}$ and (2) $I(x) <
\infty$ for all $x \in \overline{B}$, then the sequence of conditional measures
satisfies a large deviation principle with the good, effectively continuous
rate function $I_B$, where $I_B(x) = I(x)-\inf I(B)$ if $x\in\overline{B}$ and
$I_B(x) = \infty$ otherwise.
