I have been taught the definition of PWC function for a finite interval where there will be a finite number of discontinuities. But in the context of Laplace transformations, for checking sufficient conditions for the existence of a transformations but we weren't given a new definition for an infinite intervals [0,\infty]. I think the definition might be extended by saying the discontinuities are countably infinite ? I couldn't find it in my textbook or online ( I might have missed it ).
Another question I had was should the limit of the function exist at both the endpoints or just 0 ?