On Bernoulli convolutions generated by second Ostrogradsky series and their fine fractal properties

We study properties of Bernoulli convolutions generated by the second Ostrogradsky series, i.e., probability distributions of random variables ξ = ∑ k = 1 ∞ ( - 1 ) k + 1 ⁢ ξ k q k , see text ξ=∑ₖ₌₁∞{(-1)ᵏ⁺¹ξₖ}{qₖ}, where q k {qₖ} is a sequence of positive integers with q k + 1 ≥ q k ⁢ ( q k + 1 ) {qₖ₊₁≥ qₖ(qₖ+1)} , and { ξ k } {\{ξₖ\}} are independent random variables taking the values 0 and 1 with probabilities p 0 ⁢ k {p₀ₖ} and p 1 ⁢ k {p₁ₖ} respectively. We prove that ξ has an anomalously fractal Cantor-type singular distribution ( dim H ⁡ ( S ξ ) = 0 {H(Sξ)=0}