\|\widehat{u}\|\in L^{\infty}(\Omega)\}.$ One can define the spaces $\mathcal {L^{\infty}}(\Omega,X)$ and $L^{\infty}(\Omega,X)$ with real-valued norms $\|u\|_{\mathcal
L^{\infty}(\Omega,X)}=\sup\limits_{\omega\in
\Omega}|u(\omega)|_{X(\omega)}$ and $\|\widehat{u}\|_{\infty}=\bigg\|\|\widehat{u}\|\bigg\|_{L^{\infty}(\Omega)},$ respectively.

Let $X,Y$ be measurable bundles of Banach spaces. A set linear operators $\{T(\omega) : X(\omega)\rightarrow
 Y(\omega)\}$ is called *measurable bundle of linear operators* if $T(\omega)(u(\omega))$ is measurable section for any measurable section $u$.

Let $(X,L)$ be a measurable bundle of Banach spaces. If each $X(\omega)$ is a noncommutative $L_p$-space, i.e. $X(\omega)=L_p(M(\omega),\tau_\omega)$, associated with finite von Neumann algebras $M(\omega)$ and with strictly normal numerical trace $\tau_\omega$ on $M(\omega)$, then the measurable bundle $(X,L)$ of Banach spaces is called *measurable bundle of noncommutative $L_p$-spaces*.

\[1.2\][@GaC] There exists a measurable bundle $(X,L)$ of noncommutative $L_p$-spaces $L_p(M(\omega),\tau_\omega)$, such that $L_0(\Omega,X)$ is Banach —Kantorovich $*$-algebroid, which is isometrically and order $*$-isomorph to $L_p(M,\Phi)$. Moreover, the isometric and order $*$-isomorphism $H: L_p(M,\Phi)\rightarrow L_0(\Omega,X)$ can be chosen with the following propertires\

1.  $\Phi(x)(\omega) = \tau_\omega(H(x)(\omega))$ for all $x\in M$ and for almost all $\omega\in\Omega$;\

2.  $x\in M$ if and only if $H(x)(\omega)\in
     M(\omega)$ a.e. and there exist positive number $\lambda>0$, that $\|H(x)(\omega)\|_{M(\omega)}\leq\lambda$ for almost all $\omega$;\

3.  $z\in Z$ if and only if $H(z)=(\widehat{z(\omega)\mathbf{1}_\omega)}$ for some $\widehat{z(\omega)}\in L_\infty(\Omega)$, where $\mathbf{1}_\omega$ — unit of algebra $M(\omega)$, in particular 