3 More spelling correction, wp link

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 Skorohod Skorokhod topology, or something weaker than uniform.

2 Correct spelling, compact -> precompact

# Is there an extension of the arzela-ascoliArzela-Ascoli theorem to spaces of discontinuous functions?

The Arzela-Ascoli function basically says that a set of real-valued continuous functions on a compact domainis 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 cadlag 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 Skorohod topology, or something weaker than uniform.

1

# Is there an extension of the arzela-ascoli theorem to spaces of discontinuous functions?

The Arzela-Ascoli function basically says that a set of real-valued continuous functions on a compact domainis compact 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 cadlag 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 Skorohod topology, or something weaker than uniform.