  A function in a class $\mathcal{F}(X)$ is said to be subdifferentially
determined in $\mathcal{F}(X)$ if it is equal up to an additive constant to any
function in $\mathcal{F}(X)$ with the same subdifferential. A function is said
to be subdifferentially representable if it can be recovered from a
subdifferential. We identify large classes of lower semicontinuous functions
that possess these properties.
