  The paper is a sketch of systematic presentation of distributional limit
theorems and their refinements for compound sums. When analyzing, e.g., ergodic
semi-Markov systems with discrete or continuous time, this allows us to
separate those aspects that lie within the theory of random processes from
those that relate to the classical summation theory. All these limit theorems
are united by a common approach to their proof, based on the total probability
rule, auxiliary multidimensional limit theorems for sums of independent random
vectors, and (optionally) modular analysis.
