The Graham McCarthy theorem

The Graham–McCarthy theorem is a result in mathematics that characterizes when certain functions, known as "positive definite functions," can be used to build valid covariance functions in statistical models, particularly in spatial and temporal data analysis. Essentially, it provides criteria to determine if a function will produce meaningful and consistent measures of similarity or dependence between points in space or time. This helps statisticians and mathematicians ensure their models accurately represent real-world relationships, maintaining mathematical consistency and robustness in their analyses.