Construction of $R^4$ Terms in N=2 D=8 Superspace

Using linearized superfields, $R^4$ terms in the Type II superstring effective action compactified on $T^2$ are constructed as integrals in N=2 D=8 superspace. The structure of these superspace integrals allows a simple proof of the $R^4$ non-renormalization theorems which were first conjectured by Green and Gutperle.