I was just solving several problems and get stuck into the one with some weird notation. I wasn't able to understand it, though I know the meaning behind the character (angle bracket) in more broader context.
The ambiguity is with the angle bracket. Is it the integral of $h(x)$ over $p_{\beta}$? I want to be just sure.
This notations means the average of $h(x)$ over the distribution $p_{\beta}$. Written out in terms of an integral $$\langle h(x)\rangle_{p_{\beta}}=\int_{-\infty}^{\infty}h(x)p_{\beta}(x)dx$$ In general, an average of a function over a distribution is the integral of the function and the distribution over the domain of the distribution.
