3 problems

Let $X$ be the space and let $\vphi_L$, $\psi$, $\ell$, $\spH$, $\spE$, $\sigma$, $\sigma_{\operatorname{mlc}}$, $\lcc$, $\multidl_{}\paren{\vphi_L}$, and $\RTF|\cdot|(t)[\sigma]$…

Let $D\subset\mathbb{C}^n$ be a domain, and let $\varphi$ be a strongly upper semi-continuous function on $D$, meaning that for every $x\in D$ and every subset $S\subset D$ of meas…

Let $X$ be a compact Kähler manifold, let $H\to X$ be a holomorphic line bundle, and let $Z\subset X$ be a smooth hypersurface. Let $h$ be a singular Hermitian metric on $H$ satisf…