The Completion of Ã…-measure

Abstract

The theory of measure is an important subject in mathematics; in Ash [4,5]
discusses many details about measure and proves some important results in measure
theory.
In 1986, Dimiev [7] defined the operation addition and multiplication by real
numbers on a set E = (− ¥,1)Ì R , he defined the operation multiplication on the set E
and prove that E is a vector space over R and for any a>1 Ea is field, also he defined
the fuzzifying functions on arbitrary set X.
In 1989, Dimiev [6] discussed the field Ea as in [7] and defined the operations
addition, multiplication and multiplication by real number on a set of all fuzzifying
functions defined on arbitrary set X, and also defined Ã…-measure on a measurable
space and proved some results about it.
we mention the definition of the field a E , and the fuzzifying functions on the
arbitrary set X also we mention the definition of the operations.