2 problems

For a linear function space $\mathbb{X}(\mathbb{R}^n)\subset C(\mathbb{R}^n)$, a Finiteness Principle asserts that there are $k\in\mathbb{N}$ and $C>0$ such that, for every finite…

Let $E\subset\mathbb{R}^n$ be compact, let $f:E\to\mathbb{R}$, and let $M>0$ and $\eta\geq 0$. Assume that there are constants $k^\#\in\mathbb{N}$ and $C_1>0$ depending only on $n$…