Krivine schemes are optimal
Krivine schemes are optimal
It is shown that for every $k\in \mathbb {N}$ there exists a Borel probability measure $\mu$ on $\{-1,1\}^{\mathbb {R}^{k}}\times \{-1,1\}^{\mathbb {R}^{k}}$ such that for every $m,n\in \mathbb {N}$ and $x_1,\ldots , x_m,y_1,\ldots ,y_n\in \mathbb {S}^{m+n-1}$ there exist $x_1â,\ldots ,x_mâ,y_1â,\ldots ,y_nâ\in \mathbb {S}^{m+n-1}$ such that if $G:\mathbb {R}^{m+n}\to \mathbb {R}^k$ is …