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

Local Martingale

Lp Martingale

Martingale

Martingale Convergence Theorem

Martingale Equivalence for Stopping Times

Stopped Process is also R.C. Martingale

Submartingale

Supermartingale

Upcrossings