Working with sets of infinite \(\Psi _t\) -Hausdorff measures can be cumbersome, so simplifying them to sets of positive finite general fractal measures proves to be highly beneficial. This paper aims to demonstrate that the \(\Psi _t\) -Hausdorff measures adhere to the property of being a subset of positive and finite measures. Our main result is then applied to establish that the general fractal function dimension is defined as the supremum of the general fractal dimension across all Borel probability measures.
