In the article "LTC constant rate distance and locality" (link: https://arxiv.org/pdf/2111.04808.pdf), right after Lemma 2.1, the writer define the next:
Let $D$ be any probability distribution over a finite set $V$, and define an inner product by: $$\langle \cdot ,\cdot \rangle_D :\mathbb{R}^V \times \mathbb{R}^V \mapsto \mathbb{R}\quad\text{by}\quad\langle f,f'\rangle_D =\mathbb{E}_{x \sim D}(f(x)f'(x))$$
Now, I'm not sure about the meaning of the word distribution here, but the author gives the next example: Given a subset of $V$, say $T\subset V$, and denote $\mathbb{1}_T$ the indicator function over $T$, then $\langle 1_T,1_T\rangle= \mathbb{P}_D(T)$.
Any help will be appreciated :)