Let $u$, $w$ be nonnegative continuous functions such that $\frac{u}{w}$ is bounded on $B_{2^{-1}}$. Why the inequality $$a_k \le \frac{u}{w} \le b_k \quad \text{ on $B_{2^{-k}}$} , \qquad b_k - a_k < \delta^k, $$ ($\delta < 1$) for every $k \in \mathbb{N}$ implies that $\frac{u}{w}$ is Holder continuous on $B_{2^{-1}}$?

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