An Analytic Representation of the $L_0$-Valued Homomorphisms in the Orlicz–Kantorovich Modules

We consider the Orlicz–Kantorovich modules $L_M(\nabla,m)$ associated with a complete Boolean algebra $\nabla$, an $N$-function $M$, and a measure $m$ defined on $\nabla$ and taking values in the algebra $L_0$ of all measurable real functions. We obtain an analytic representation of the continuous $L_0$-valued homomorphisms defined on such modules.