For starters, I've studied following maths:
Linear Algebra
Rudin's PMA
Stein's Real Analysis (upto ch4: Intro to Hilbert Space)
other basic statistics subjects (mathematical statistics, regression analysis, etc)
I was given the following paper regarding high-dimensional least squares, and I was trying to understand the theorem 1 of the paper (appendix C.2 page 39).
The thing is, I was stuck to the following statement.
$$V_X(\hat \beta;\beta) = \frac{\sigma^2}{p}\sum_{i=1}^n\frac{1}{t_i}
= \frac{\sigma^2 n}{p}\int \frac{1}{t}dF_{XX^T/p}(t),$$
where $F_{XX^T/p}$ is the spectral measure of $XX^T/p$.
I've seen the term spectral measure for the first time, so I tried to look several functional analysis books (including Rudin's functional analysis, and Kreyszig's Introductory Functional Analysis with Applications), but I failed to find the term spctral measure.
It would be grateful if you recommend some textbooks covering spectral measure. If my math basic is not enough to understand it, could you also recommend me about what I should study before understanding spectral measure?
Thank you in advance.