In this article, we introduce algebras of random measures. Algebra is a vector space
V
V
over a field
F
F
with a multiplication satisfying the property: 1) distribution and 2)
c
(
x
⋅
y
)
=
(
c
x
)
⋅
y
=
x
⋅
(
c
y
)
c(x\cdot y) = (cx)\cdot y = x\cdot (cy)
for every
c
∈
F
c \in F
and
x
,
y
∈
V
x, y \in V
. The first operation is a trivial addition operation. For the second operation, we present three different methods 1) a convolution by covariance method, 2) O-dot product, 3) a convolution of bimeasures by Morse-Transue integral. With those operations, it is possible to build three different algebras of random measures.