The Arzela-Ascoli function basically says that a set of real-valued continuous functions on a compact domain is precompact under the uniform norm if and only if the family is pointwise bounded and equicontinuous.

Are there any analogs of this kind of result for spaces of noncontinuous functions? The specific set I have in mind is the càdlàg functions, which are right continuous and have left limits. Essentially, I want to know if there is any relationship between compactness and equicontinuity. Here, equicontinuity would obviously have to be relaxed to account for jumps, and compactness in the uniform topology could be relaxed to compactness in, say, the Skorokhod topology, or something weaker than uniform.