  In this paper, based on the initiation of the notion of negatively associated
random variables under nonlinear probability, a strong limit theorem for
weighted sums of random variables within the same frame is achieved without
assumptions of independence and identical distribution, from which the
Marcinkiewich-Zygmund type and Kolmogorov type strong laws of large numbers are
derived. In addition, as applications of our results, Stranssen type invariance
principles of negatively associated random variables and vertically independent
random variables are proposed respectively.
