= Geometric bound for omitted Haar details
{title2=$\sum_{j=J}^{K}\delta/\sqrt{L2^{-j}}\leq\frac{\delta2^{K/2}/\sqrt L}{1-2^{-1/2}}$}
At each point there is at most one supported <Haar wavelet> per scale. If a detail coefficient is below $\delta$, its value there is at most $\delta2^{j/2}/\sqrt L$. Summing these bounds up to level $K$ gives the displayed geometric estimate. Selecting $K$ so the final term is of the order of the <modulus of continuity> controls all omitted fine details, even though arbitrary deletions from a uniformly convergent series need not preserve convergence.
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