Abstract
The aim of measurement is to obtain quantitative knowledge about properties of things or of fields. The knowledge is evaluated from the viewpoint of information theory. The average amount of information obtained by taking readings of an analog measuring instrument is calculated as the difference of the a-priori entropy and a-posteriori one both of which are functions of the scale interval of the indicating instrument and the standard deviation of the measurement system. The average amount of information does not increase unlimitedly but tends to a finite value as the scale interval is diminished, unless the standard deviation of the system is zero.
In a duplicate measurement, the average amount of information obtained from the second reading is far smaller than that obtained from the first reading, but the total average amount of information is shown equal to that obtained by a single measurement with a system the standard deviation of which is √2 times as small.
