Bernstein polynomial

For $f\in C([0,1{]}^d)$, its tensor-product Bernstein polynomial is the expectation of $f(X_1/n,\dots ,X_d/n)$ for independent binomial variables $X_j\sim \mathrm{Bin}(n,x_j)$. Uniform continuity and concentration of the binomial variables prove uniform convergence to $f$.