Outside of the zero measure and counting measure, what are some examples of of measures over the space $L^2(\Omega)$ where $\Omega$ is some subset of $\mathbb{R}^n$? Mostly, I'm looking for concrete examples of measures in infinite dimensional space outside of stochastic measures like the Gaussian measure. Certainly, as this question answered:
there's not a Lebesgue-like measure. I'm really just looking for a combination of both simple and moderately interesting examples.