Hold on.

The first lesson in Probability Theory class is the following.

Whenever you approach a problem, the first thing you should do is to define a probability space. If the probability space is not defined, then all these concepts don't make sense. There is no "probability", there is no "expectation" and "divergence". Also there is no "entropy" and "Shanon entropy".

The probability space has not been defined in the paper. If the choice of the probability space is obvious, then you can easily fill this gap and define probability space instead of the author.