We provide here a novel algebraic characterization of two information measures associated with a vector-valued random variable, its differential entropy and the dimension of the underlying space, purely based on their recursive properties (the chain rule and the nullity-rank theorem, respectively). More precisely, we compute the information cohomology of Baudot and Bennequin with coefficients in a module of continuous probabilistic functionals over a category that mixes discrete observables and continuous vector-valued observables, characterizing completely the 1-cocycles; evaluated on continuous laws, these cocycles are linear combinations of the differential entropy and the dimension.

翻译：更准确地说,我们计算了Baudot和Bennequin的信息共生学,在连续概率功能模块中的系数,该模块混合了离散可观测值和连续可观测值的可观测值,将一个循环周期完全定性;根据连续法评估,这些共生周期是不同导体和维度的线性组合。