I am seeking for a great book on graduate-level, measure-theory based book on stochastic process, the ones I can find are this book by Cosma Rohilla Shalizi and Aryeh Kontorovich, and Foundations of Modern Probability
I can find a lot of classic book on stochastic process, like Stochastic Processes by Ross, and Introduction to Stochastic Processes by Lawler, but they do not have a measure-theoretic framework, so I wonder if there are some well recognized book in this area?