This paper establishes the existence of global random attractors for random dynamical systems (RDS). It proves that invariant Markov measures supported by the random attractor exist, and applies these results to reaction-diffusion equations with additive white noise and Navier–Stokes equations with both multiplicative and additive white noise. The main result is a theorem showing that under certain conditions, a global attractor exists for an RDS on a Polish space. The attractor is shown to be compact and to attract all bounded subsets of the state space. The paper also discusses the existence of invariant measures for the associated Markov semigroup and applies these results to specific examples. The paper concludes with a discussion of the properties of global attractors, including their connection to invariant measures and their role in the study of stochastic systems.This paper establishes the existence of global random attractors for random dynamical systems (RDS). It proves that invariant Markov measures supported by the random attractor exist, and applies these results to reaction-diffusion equations with additive white noise and Navier–Stokes equations with both multiplicative and additive white noise. The main result is a theorem showing that under certain conditions, a global attractor exists for an RDS on a Polish space. The attractor is shown to be compact and to attract all bounded subsets of the state space. The paper also discusses the existence of invariant measures for the associated Markov semigroup and applies these results to specific examples. The paper concludes with a discussion of the properties of global attractors, including their connection to invariant measures and their role in the study of stochastic systems.