  The purpose of this paper is to clarify the (non-Bayesian and Bayesian)
two-envelope problems in terms of quantum language (or, measurement theory),
which was recently proposed as a linguistic turn of quantum mechanics (with the
Copenhagen interpretation). The two envelopes paradox is only a kind of high
school student's probability puzzle, and it may be exaggerated to say that this
is an unsolved problem. However, since we are convinced that quantum language
is just statistics of the future, we believe that there is no clear answer
without the description by quantum language. In this sense, the readers are to
find that quantum language provides the final answer (i.e., the easiest and
deepest understanding) to the two envelope-problems in both non-Bayesian and
Bayesian statistics. Also, we add the discussion about St. Petersburg
two-envelope paradox.
