It is a basic concept in Lebesgue measure (theorem) to separate discrete and continuous parts.
Although data is usually finite and hence can be viewed as discrete, its quantity very often explodes and we may assume that the data is "continuous"Â (i.e. there are enough samples to interpolate (or extend) it everywhere in its domain).
The best illustration of this idea is the fact that the basic MNIST dataset can be predicted with 98% accuracy (see second row here) just from "learning" locations of background (i.e. values 0) and high values (close to 255). Notice that the dataset contains 28x28 images with values between 0-255 for each pixel, which are labeled between 0-9 corresponding to the digit each image represents. For more details read in Discrete Part page.