Using Vector Representations of Characteristic Functions and Vector Logarithms When Proving Asymptotic Statements

In this methodological–technical note, in addition to the well-known concepts of logarithms of positive real numbers and operators, we open a path for mathematical treatment of the mathematical concept of the logarithm of a vector. We prove the most basic arithmetic operations for this new logarithm concept and demonstrate how it applies to characteristic functions and limit theorems of probability theory. As a side result, we revise a formula for ii that is known from the literature.