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Results tagged with limsup-and-liminf
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user 91890
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.
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How can we show that if $f$ is convex, then $\liminf_{|x|\to\infty}\frac{x\cdot\nabla f(x)}{...
Let $d\in\mathbb N$ and $f:\mathbb R^d\to\mathbb R$ be convex with $$\int e^{-f(x)}\:{\rm d}x<\infty\tag1.$$ How can we show that $$\liminf_{|x|\to\infty}\frac{x\cdot\nabla f(x)}{|x|}>0?$$ $f$ should …
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