ON BOREL’S TYPE RELATION FOR THE LAPLACE-STIELTJES INTEGRALS - Скасків, Олег Богданович; Тарновецька, Ольга Юріївна; Трусевич, Оксана Мирославівна (PRECARPATHIAN BULLETIN OF THE SHEVCHENKO SCIENTIFIC SOCIETY. Number, 2019)
In article it is obtained sufficient conditions in order that relation F(x)(1+o(1))μ(x,F) holds for each function of the form F(x)=_n=0^+∞ f_n e^xλ_n +τ(x)β_n as x→ +∞ outside some set E of zero linear density or of zero lower linear density, where (f_n), (λ_n), (β_n) are positive sequences, and a differentiable function τ: R_+→ R_+ such thatτ′(x) 1 (xx_0), μ(x,F)={ f_ne^xλ_n +τ(x)β_n: n 0} .