All Questions

Does the following integration method hold for regular enough functions $F:\mathbb{R}\to\mathbb{R}$? \begin{align} &\zeta(2)\sum_{\frac{a}{b}\in\mathbb{Q}_n} \frac{F(\log \frac{a}{b})}{\sqrt{abn}...

I am trying to simplify the following limit of integral where $\mu$ is given: $$p(y) = \lim_{\sigma \to 0} \int_{\mathbb R} |x| \cdot \frac{1}{\sqrt{2\pi\sigma^2} } e^{-\frac{1}{2\sigma^2} (xy - \mu)^...

Suppose $(X,B,m)$ is a finite measure space and $(f_n)$ is a sequence of functions converging almost surely and in $L^2(X,m)$. Moreover, I know that for every $n$, $\int e^{f_n(x)} m(dx)<\infty$. ...

Let $X$ be a space endowed with a finite measure $m$. Let $f_n : \to \mathbb C$ be measurable functions such that $|f_n| \le 1$ for all $n$ and $f_n \to 0$ in every space $L^p (X)$ with $p \in [1, \...

The set of HK integrable functions with an integrable upper bound $f$ forms a lattice, and satisfies the MCT and DCT. Does this mean that the lattice is countably complete? Indexing any countable set, ...

I am struggling to understand the proof in the paper, Learning Temporal Evolution of Spatial Dependence with Generalized Spatiotemporal Gaussian Process Models. Theorem 2.1 in the page 33 uses ...