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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 ...

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, ...

Consider a function sequence $\{f_n(t)\}$ ($n\in\mathbb{N}^+$) defined on the interval $(\frac{1}{2},1)$, where \begin{eqnarray}\label{eqn:constraint1} f_n(t)=\frac{\exp\left(n\left(\log R(h_t) - th_t\...

Let $f_n$ be a sequence of $L^1(]0,1[)$ functions such that $f_n$ is non-decreasing, at least left-continuous, $f_n(0^+) <0$, $f_n(1^-) >0$, for all $n \in \mathbb N$. This sequence converges $...

I'm looking for the following limit: $$\lim_{\varepsilon\to 0^+}\int_{-\sqrt{\varepsilon}}^{\sqrt{\varepsilon}}\frac{1}{\sqrt{2\pi}\varepsilon^{3/2}}\left(-1+\frac{x^2}{\varepsilon}\right)e^{-\frac{x^...