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The article examines the probability and integral solutions to the fixed Kolmogorov equation, L*μ = 0. It analyzes the circumstances that probability solutions are given unique integral solution up to multiplication by a constant. It notes that the uniqueness in the class of probability solutions and the uniqueness in the class of integrable solutions are varied constructs that are already in dimension d = 1. It considers the validity of the given theorems, asserting that theorems 3 and 5 need additional conditions on the manifold.

The article discusses the integration of functions rd-continuous on time scales. The notes the development of the theory of dynamic equations on time scales which aims to establish a uniform theory of ordinary differential equations with discontinuous argument. It explains that the definition of integral invokes doubts in the rightness of results based on an integration method. It reveals the availability of an approach to differential equations on time scales according to a natural extension of solutions on the corresponding general integral theory adaptation.