One can recover vectors from $\mathbb{R}^m$ with arbitrary precision, using only $\lceil \log_2(m+1)\rceil +1$ continuous measurements that are chosen adaptively. This surprising result is explained and discussed, and we present applications to infinite-dimensional approximation problems.

翻译：仅需使用$\lceil \log_2(m+1)\rceil +1$次自适应选择的连续测量，即可从$\mathbb{R}^m$中以任意精度恢复向量。本文解释并讨论了这一令人惊讶的结果，并展示了其在无限维逼近问题中的应用。