Measurement theory describes the methodology associated with the relation of numbers and mathematical operations to physical objects and processes. In a very practical sense, measurement theory deals with mathematical measurement and the analysis of mathematical measurement. A key component of mathematical analysis is error analysis that allows the estimations of measurement accuracy and precision. The development of measurement theory also involves justification of measurement and estimation of uniqueness of the measurement of physical phenomena. Measurements are considered unique if there is only one possible way to mathematically characterize the phenomena.

Measurement theory is as ancient as formalized mathematics. Aspects of measurement theory were included in Euclid's elements and since that time measurement theory has evolved critical axioms that form the basis of modern data analysis. Measurement theory itself is broadly described as the set of rules related to the quantitative measurement of properties of physical entities...