Axiom 1. [=measurement axiom (Observable, Measured value, Measurement, Probability)] The measurement of the observable O for the system S with the state ω is denoted by $M_{C\left(\Omega \right)}\left(O:=\left(X,\mathcal{P}\left(X\right),G\right),S_{\left[\omega \right]}\right)$ . An observer can obtain a measured value $x\left(\in X\right)$ by the measurement $M_{C\left(\Omega \right)}\left(O,S_{\left[\omega \right]}\right)$ . And the probability that a measured value $x\left(\in X\right)$ obtained by the measurement $M_{C\left(\Omega \right)}\left(O,S_{\left[\omega \right]}\right)$ is given by [G({x})](ω).