  A theory of martingales for censoring is developed. The Doob-Meyer martingale
is shown to be inadequate in general, and a repaired martingale is proposed
with a non-predictable centering term. Associated martingale transforms,
variation processes, and covariation processes are developed based on a measure
of half-predictability that generalizes predictability. The development is
applied to study the Kaplan Meier estimator.
