Infinitesimal analysis. Part 2. (Q2744694)

[For Part I, see Zbl 1013.46003 above.]NEWLINENEWLINENEWLINEThis is the second part of the book dedicated to set-theoretic formalisms that allow us to use actual infinitely large and actual infinitesimal quantities. Applications of infinitesimal methods in topology, measure theory, optimization, and harmonic analysis are studied in detail. NEWLINENEWLINENEWLINEThe contents of the second part of the book is as follows. Chapter 6 ``Technique of hyperapproximation'' (pp. 1--74) addresses the problem of approximating infinite-dimensional Banach spaces and operators between them by finite-dimensional spaces and finite-rank operators. Naturally, some infinitely large number plays the role of the dimension of such an approximate space. Chapter 7 ``Infinitesimals in harmonic analysis'' (pp. 75--182) provides the details of the nonstandard technique for `hyperapproximation' of locally compact abelian groups and Fourier transforms over them. Chapter 8 ``Exercises and unsolved problems'' (pp. 183--199) collects some exercises for drill and better understanding as well as several open questions whose complexity varies from nil to infinity. Appendix (pp. 200--205) contains a short essay on Boolean-valued models of set theory. The list of references (pp. 206--241) contains 533 items.