Asymptotics of the Partition of the Cube into Weyl Simplices and an Encoding of a Bernoulli Scheme

We suggest a combinatorial method for encoding continuous symbolic dynamical systems. We transform a continuous phase space, the infinite-dimensional cube, into the path space of a tree, and the shift corresponds to a transformation which we called “transfer.” The central problem is that of distinguishability: does the encoding distinguishes between almost all points of the space? The main result says that the encoding by means of the partition of the cube into Weyl simplices has this property.