Quasi-invariant and invariant functionals and measures on systems of topological loops and quasigroups

Under study are the left-invariant, right-invariant, and quasi-invariant functionals and measures on topological loops and quasigroups. We also address the relations between topologies and measures on loops, the left-invariant, right-invariant, and quasi-invariant functionals and measures on locally connected as well as profinite loops and quasigroups. Moreover, we inspect how the quasi-invariant measures on topological spaces are related to the loop or quasigroup actions on them. Also, we consider the continuations of quasi-invariant functionals and measures on the extensions of topological spaces as well as measures and functionals on the inverse spectra of topological loops and quasigroups.