A semimeasure on the set of finite binary strings is a nonnegative function 
satisfying
 |  |
(1)
| |
 |  |  |
(2)
|
for every string 
, where 
is the empty string. Equality
in the second relation gives the consistency condition for a probability
measure on infinite binary sequences. The possible
deficit allows probability mass to terminate at a
finite string. Universal lower semicomputable semimeasures
are used in algorithmic probability.
