Abstract
Absolutely continuous functions are an important class of functions for both applications and theory. Every polynomial of a finite order as well as every differentiable function is absolutely continuous. Moreover, any solution of an ordinary differential equation is absolutely continuous, since the latter is at least one times differentiable. These examples are not exhaustive. In this chapter, we consider conditions under which absolutely continuous functions belong to the classes PRV, PI, SQI, or POV (see Definitions 3.16–3.32). The results obtained in this chapter will be used throughout the book, for example, in Chaps. 5–9.
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Buldygin, V.V., Indlekofer, KH., Klesov, O.I., Steinebach, J.G. (2018). Properties of Absolutely Continuous Functions. In: Pseudo-Regularly Varying Functions and Generalized Renewal Processes. Probability Theory and Stochastic Modelling, vol 91. Springer, Cham. https://doi.org/10.1007/978-3-319-99537-3_4
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