Kantorovich polynomials

Summary

Kantorovich polynomials are a variant of Bernstein polynomials that use averages of $f$ over small intervals instead of point values. Because they only need integrals, they are defined for every integrable function on $[0, 1]$. They converge to $f$ in the $L^p$ norm for $1 \le p < \infty$. This makes sense for elements of $L^p$, where point values are not defined.