for a wide class of functions "f" (namely: all continuous functions; all locally integrable functions; all non-negative measurable functions). The density "Lt" is (more exactly, can and will be chosen to be) continuous. The number "Lt"("x") is called the local time at "x" of "w" on "t". It is strictly positive for all "x" of the interval ("a", "b") where "a" and "b" are the least and the greatest value of "w" on "t", respectively. (For "x" outside this interval the local time evidently vanishes.) Treated as a function of two variables "x" and "t", the local time is still continuous. Treated as a function of "t" (while "x" is fixed), the local time is a singular function corresponding to a nonatomic measure on the set of zeros of "w".