The majorizing measure theorem of Fernique and Talagrand is a fundamental result in the theory of random processes. It relates the boundedness of random processes indexed by elements of a metric space to complexity measures arising from certain multiscale combinatorial structures, such as packing and covering trees. This paper builds on the ideas first outlined in a little-noticed preprint of Andreas Maurer to present an information-theoretic perspective on the majorizing measure theorem, according to which the boundedness of random processes is phrased in terms of the existence of efficient variable-length codes for the elements of the indexing metric space.

翻译：费尔南克（Fernique）与塔拉格兰德（Talagrand）提出的控制测度定理是随机过程理论中的一项基础性成果。该定理建立了由度量空间元素索引的随机过程的有界性与源自某些多尺度组合结构（如包装树和覆盖树）的复杂性度量之间的联系。本文基于安德烈亚斯·毛雷尔（Andreas Maurer）一篇鲜为人知的预印本中首次概述的思想，提出对控制测度定理的信息论视角：根据该视角，随机过程的有界性可表述为索引度量空间元素存在高效变长编码的条件。