A simple proof that determinacy implies Lebesgue measurability.
We present a simplified integral of functions of several variables. Although less general than the Riemann integral, most functions of practical interest are still integrable. On the other hand, the basic integral theorems can be obtained more quickly. We also give a characterization of the integrable functions and their primitives.
Given a two-dimensional fractional multiplicative process determined by two Hurst exponents and , we show that there is an associated uniform Hausdorff dimension result for the images of subsets of by if and only if .