  In this note, it is shown that the stochastic Airy operator, which is the
"Schr\"odinger operator" on the half-line whose potential term consists of
Gaussian white noise plus a linear term tending to $+\infty$, can naturally be
defined as a generalized Sturm-Liouville operator and that it is self-adjoint
and has purely discrete spectrum with probability one. Thus "stochastic Airy
spectrum" of Ram\'irez, Rider and Vir\'ag is the spectrum of an operator in the
ordinary sense of the word.
