Some results for probability
measures on function spaces are extended to finite signed measures (FSM’s). In
particular FSM’s on the space of continuous functions and right-continuous functions
with left-hand limits are patched together by a procedure of Stroock and
Varadhan. Given an increasing sequence of stopping times the procedure is
carried out repeatedly. A sequence of transition functions and, an extension
result for the linear maps associated with these transition functions are
obtained.