ON STOCHASTICALLY INDEPENDENT CONTINUOUS FUNCTIONS

摘要

We discuss continuous functions that are stochastically independent as random variables. It is shown that such functions are closely related to Peano curves which fill parallelotopes in Euclidean spaces. An explicit construction of independent functions is presented which leads to a sufficiently complete description of collections of stochastically independent continuous functions on an interval. Several related results are also presented and a few open problems are formulated.