  The central limit theorem of martingales is the fundamental tool for studying
the convergence of stochastic processes. The central limit theorem and
functional central limit theorem are obtained for martingale like random
variables under the sub-linear expectation by Zhang (2019). In this paper, we
consider the multi-dimensional martingale like random vectors and establish a
functional central limit theorem. As applications, the Lindeberg central limit
theorem for independent random vectors is established, and the sufficient and
necessary conditions of the central limit theorem for independent and
identically distributed random vectors are obtained.
