= Haar projection error for a Lipschitz function
{c}
{title2=$\|K_jf-f\|_\infty\le L2^{-j}$}
The <Haar projection> replaces a <function> by its mean on each <dyadic interval> of length $2^{-j}$. For a function satisfying <Lipschitz continuity> with constant $L$, every value in a cell differs from its cell mean by at most $L2^{-j}$. This bound holds for all points with a consistent endpoint convention, and requires no global <L2 norm> assumption when the projection is defined by local averages.
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