Paper detail

Normal and pseudonormal numbers

After a short review of the historical milestones on normal numbers, we introduce the Borel numbers as the reals admitting a probability function on their different bases representations. In this setting, we provide two probabilistic characterizations of normality based on the stochastic independence of their digits. Finally, we define the pseudonormality condition, which is satisfied by normal numbers and may be evaluated in a finite number of steps.