Notation of sequences in rate distortion theory
In information theory notation, capital letters such as $X$ denote random variables, and lowercase letters such as $x$ mean their possible outcomes (i.e., fixed values). For example you can write the definition of expectation as $E[X] = \sum p(x) \cdot x$. Moreover, vector values are denoted using length as superscripts, for example $X^n$ means $(X_1, \ldots, X_n)$ (similarly for $x^n$). Moreover a substring $(X_i, \ldots, X_j)$ is often denoted by $X_i^j$. These slides seem to be consistent with this convention.