The Gibbs Measure is a probability distribution used in statistical mechanics to describe the behavior of systems in thermal equilibrium. It assigns probabilities to different configurations of a system based on their energy levels, following the principle that lower energy states are more likely to occur. This measure is particularly useful for understanding phase transitions and collective behaviors in large systems. In mathematical terms, the Gibbs Measure is defined using the Boltzmann factor, which incorporates the temperature of the system and the energy of each configuration. It is closely related to concepts in thermodynamics, Markov random fields, and statistical physics, providing a framework for analyzing complex systems in various fields, including mathematics and computer science.