Gusein-Zade's Betti-density conjecture for quasiperiodic functions

Let $f$ be a quasiperiodic function, and let $b_f^k(c)$ denote the density of its $k$-th Betti number at level $c$, defined by averaging the corresponding Betti number over expanding balls when the limit exists. Gusein-Zade's conjecture. For all analytic (respectively, almost all smooth) quasiperiodic functions, the Betti-number densities are well defined. The source explicitly says that this was proved in the smooth case for the Betti-number densities by A. I. Esterov in 2000, so the conjecture is resolved at least in that stated smooth setting.