Methods of Renormalization and Distributions

In this article, we consider the mathematical meaning of renormalization. We show that divergent integrals can be given finite values in the case of conditional convergence of extended integrals by subtracting an infinite quantity. This can be considered as a kind of renormalization of divergent integrals. Using this method of renormalization, we define distributional extensions of measurable functions with nonsummable singuralities