be written as $$\tilde {M} _{s,t} = \delta _{(u_{1}, v_{1}), (u_{2}, v_{2})}^{(2)} \left(1_{[0,s] \times [0,t] } ^{\otimes 2} ((u_{1}, v_{1}), (u_{2}, v_{2}) ) 1_{[0,u_{1} ]}(u_{2} ) 1_{[0, v_{2} ]} (v_{1}))\right).$$ Let us explain the above notation. The symbol $\delta ^{(2)} $ means the double (iterated) Skorohod integral with respect to the Wiener sheet $W$. The indices $(u_{1}, v_{1}), (u_{2}, v_{2})$ in the formula $\delta _{(u_{1}, v_{1}), (u_{2}, v_{2})}^{(2)}$ means that the double Skorohod integral acts with respect to the two variables $(u_{1}, v_{1})$ and $(u_{2}, v_{2})$.

More generally, if $(X_{s,t})_{s,t\in [0,1]}  $ is an adapted two-parameter process (let us be vague on this concept because several definitions of the adaptability exist in the two-parameter context; we refer again to [@Imk], [@N81] or [@Dozzi]), then the sequence $$\sum_{i=0}^{m-1} \sum_{j=0}^{n-1} X_{s_{i}, t_{j}}\left( W_{s_{i}, t_{j+1} }-  W_{s_{i}, t_{j} }\right) \left( W_{s_{i+1}, t_{j} }-  W_{s_{i}, t_{j} }\right)$$ converges to the integral $$\int_{0}^{t} \int_{0}^{s}  X_{u,v} dM_{u,v} = \int_{0}^{t}\int_{0} ^{s} X_{u,v} d_{u}W_{u,v} d_{v} W_{u,v}$$ which can be also written as a double Skokorod integral in the following way (assuming that $X$ is regular enough in the Malliavin calculus sense) $$\begin{aligned}
\int_{0}^{t}\int_{0} ^{s} X_{u,v} d_{u}W_{u,v} d_{v} W_{u,v}&=& \delta ^{(2)} \left( X_{u_{1},v_{2}} 1_{[0,u_{1}]}(u_{2}) 1_{[0,v_{2}] }(v_{1})\right)\end{aligned}$$ where $\delta ^{(2)} 