A null ideal for inaccessibles

In this paper we introduce a tree-like forcing notion extending some properties of the random forcing in the context of the generalised Cantor space and study its associated ideal of null sets and notion of measurability. This issue was also addressed by Shelah ([11, Problem 0.5]) and concerns the definition of a forcing which is $\kappa^kappa$-bounding, $< \kappa$-closed and $\kappa^+$-cc, for $\kappa$ inaccessible.