Continuous Martingale with Finite Variation is Constant

Doob's Forward Convergence Theorem

Doob's Maximal Inequalities

Doob's Optional Sampling Theorem

Doob's Upcrossing Inequality

Existence of Càdlàg Version

Lévy's Convergence Theorems

Martingale Convergence Theorem

Martingale Equivalence for Stopping Times

Stopped Process is also R.C. Martingale