I am confronted with the following situation/definition in the introduction of a static hedging strategy (for further information, see Henry-Labordere, Tan, Touzi: An Explicit Martingale Version of the One-dimensional Brenier's Theorem with full Marginals Constraint; section 3):
We will denote by $M([0,1])$ the space of all finite signed measure on $[0,1]$. Next we consider all measurable maps $\lambda:\mathbb{R}\rightarrow M([0,1])$ with the following representation: $\lambda(x,dt)=\lambda_0(t,x)\gamma(dt)$ where $\gamma$ is a finite non-negative measure on $[0,1]$ and $\lambda_0$ is a measurable function from $[0,1]\times\mathbb{R}$ to $\mathbb{R}$ which is bounded on $[0,1]\times K$ for compacts $K \subset \mathbb{R}$.
Do anyone has a good interpretation of this situation which is connected to static hedging strategies?