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For questions concerning limit superior and limit inferior of sequences (of real numbers and various generalizations) and also for $\limsup$ and $\liminf$ of sequences of sets.
4
votes
How can we show that if $f$ is convex, then $\liminf_{|x|\to\infty}\frac{x\cdot\nabla f(x)}{...
$\newcommand{\R}{\mathbb{R}}
\newcommand{\ep}{\varepsilon}
$
For any $x\in\R^d$, let us understand $\nabla f(x)$ as any one of the subgradients of the convex function $f$ at point $x$ (so, we will not …