Abstract (17.0: Equilibrium statistical mechanics and Ergodic Hypothesis)
In this chapter, we study and answer the following fundamental
problems concerning
classical
equilibrium
statistical mechanics:
$(A):$ 
Is the principle of equal a priori probabilities
indispensable for
equilibrium statistical mechanics?

$(B):$ 
Is
the ergodic hypothesis
related to
equilibrium statistical mechanics?

$(C):$ 
Why and where does the concept of "probability" appear in
equilibrium statistical mechanics?

Note that
there are several opinions for the formulation
of
equilibrium
statistical mechanics.
In this sense,
the above problems are not yet answered.
Thus we
propose
the measurement theoretical foundation
of
equilibrium
statistical mechanics, and clarify
the confusion between
two aspects
(i.e.,
probabilistic and kinetic aspects
in
equilibrium
statistical mechanics),
that is,
we discuss
$\bullet$ 
$
\begin{cases}
\mbox{the kinetic aspect (i.e., causality)}
&
\cdots
\mbox{ in Section 17.1}
\\
\mbox{the probabilistic aspect (i.e., measurement) }
&
\cdots
\mbox{ in Section 17.2}
\end{cases}
$

And we answer the above (A) and (B),
that is,
we conclude that
$(\sharp )$ 
(A) is "No",
but,
(B) is "Yes"

and further, we can understand the problem (C).
This chapter is extracted from the following: