Convergence rate in the law of logarithm for negatively dependent random variables under sub-linear expectations

Let \X, Xₙ, n 1\ be a sequence of identically distributed, negatively dependent (NA) random variables under sub-linear expectations, and denote Sₙ=₈=₁^nXᵢ, n 1. Assume that h () is a positive non-decreasing function on (0, ) fulfulling ₁^ (th (t) ) ^-1 t=. Write Lt= \, t\, (t) =₁^t (sh (s) ) ^-1 s, t 1. In this sequel, we establish that ₍=₁^ (nh (n) ) ^-1\|Sₙ| (1+) 2nL (n) \0 if (X) = (-X) =0 and (X²) =² (0, ). The result generalizes that of NA random variables in probability space.