Abstract: Recently we propose measurement theory, which is a kind
of quantitative language for the description of ordinary science. The purpose of
this paper is to characterize dynamical system theory and statistics in terms of
measurement theory. We first introduce the transformed measurement theory,which
is due to the Schrödinger picture. And, from the transformed measurement
theory, we construct dynamical system theory and statistics, which acquire exact
probability spaces as compensation for the abandonment of measurements. And
further we conclude, from the pure theoretical point of view, that dynamical
system theory and statistics are essentially the same. On the other hand,
measurement theory must be reconstructed in the
-algebraic formulation if exact measurements and infinite measurements are
needed.
Keywords and phrases: measurement theory, quantitative language, dynamical system theory, statistics.
