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  "body": "\n## Summary\n\nKantorovich polynomials are a variant of [[Bernstein polynomials|0JT92VK307]] that use averages of $f$ over small intervals instead of point values.\nBecause they only need integrals, they are defined for every integrable function on $[0, 1]$.\nThey converge to $f$ in the $L^p$ norm for $1 \\le p \u003c \\infty$.\nThis makes sense for elements of $L^p$, where point values are not defined.\n\n## Explanations\n\n### L1 human\n\nA Bernstein polynomial looks at $f$ only at the points $k/n$.\nIf $f$ is only known up to its values on sets of measure zero, those point values mean nothing.\nThe Kantorovich polynomial replaces the value at a point by the average of $f$ over a small interval around it.\nFor the constant $1$, every average is $1$, and the Kantorovich polynomial is again $1$.\n",
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