The existence theorem of random vector-valued measures and one in another form that is conveinent for use are showed.We substitute the two- point distribution in the expression of the thinning operator by a probabi- lity measure on (the index set may be uncountable),and obtain what we call mark accumulator mapping,its existence having been proved by use of the existence theorems mentioned above.we parallelly extend almost all properties of the thinning operator to the mark accumulator mapping.
