Axiomatic theory of divergent series and cohomological equations
Volume 198 / 2008
Fundamenta Mathematicae 198 (2008), 263-282 MSC: 40C99, 42A24, 37A30. DOI: 10.4064/fm198-3-5
A general theory of summation of divergent series based on the Hardy–Kolmogorov axioms is developed. A class of functional series is investigated by means of ergodic theory. The results are formulated in terms of solvability of some cohomological equations, all solutions to which are nonmeasurable. In particular, this realizes a construction of a nonmeasurable function as first conjectured by Kolmogorov.