= Solution
For a real <locally integrable function> $f$, the distributional definition of a <subharmonic function> is $\Delta f\geq0$: for every nonnegative $\varphi\in C_c^\infty(\Omega)$,
$$
\boxed{\int_\Omega f\,\Delta\varphi\geq0.}
$$
A <superharmonic function> has the opposite inequality, equivalently $-f$ is subharmonic. A <harmonic function> has $\Delta f=0$ distributionally, equivalently equality for every test function. These definitions concern almost-everywhere classes; the given upper semicontinuous representative supplies the pointwise version for subharmonic functions.
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