  We give an abstract approach to approximations with a wide range of
regularity classes $X$ in spaces of pseudocontinuable functions
$K^p_\vartheta$, where $\vartheta$ is an inner function and $p>0$. More
precisely, we demonstrate a general principle, attributed to A. B. Aleksandrov,
which asserts that if a certain linear manifold $X$ is dense in the space of
pseudocontinuable functions $K^{p_0}_\vartheta$, for some $p_0>0$, then $X$ is
in fact dense in $K^p_{\vartheta}$, for all $p>0$. %This allows for
generalizations of the recent result on density by functions with smooth
boundary extensions. Moreover, for a rich class of Banach spaces of analytic
functions $X$, we describe the precise mechanism that determines when $X$ is
dense in a certain space of pseudocontinuable functions. As a consequence, we
obtain an extension of Aleksandrov's density theorem to the class of analytic
functions with uniformly convergent Taylor series.
