  We discuss the problem of performing similarity search over function spaces.
To perform search over such spaces in a reasonable amount of time, we use {\it
locality-sensitive hashing} (LSH). We present two methods that allow LSH
functions on $\mathbb{R}^N$ to be extended to $L^p$ spaces: one using function
approximation in an orthonormal basis, and another using (quasi-)Monte
Carlo-style techniques. We use the presented hashing schemes to construct an
LSH family for Wasserstein distance over one-dimensional, continuous
probability distributions.
