Editing Wiener process (section)

=== Brownian martingales ===
Let ''A'' be an event related to the Wiener process (more formally: a set, measurable with respect to the Wiener   measure, in the space of functions), and ''X<sub>t</sub>'' the conditional probability of ''A'' given the Wiener process on the time interval [0, ''t''] (more formally: the Wiener measure of the set of trajectories whose concatenation with the given partial trajectory on [0, ''t''] belongs to ''A''). Then the process ''X<sub>t</sub>'' is a continuous martingale. Its martingale property follows immediately from the definitions, but its continuity is a very special fact – a special case of a general theorem stating that all Brownian martingales are continuous. A Brownian martingale is, by definition, a [[martingale (probability theory)|martingale]] adapted to the Brownian filtration; and the Brownian filtration is, by definition, the [[filtration (probability theory)|filtration]] generated by the Wiener process.