Transforming continuous utility into additive utility using kolmogorov's theorem

For a multidimensional criteria space to have an additive utility function, the strong condition of independence among the co-ordinates (also known as separability) must be satisfied. However, if we are allowed to transform the criteria space into another, then a theorem due to Kolmogorov implies that we can, even in the absence of independence, transform the space into one that has a continuous additive utility function. Since this transformation is complex, it has only theoretical significance. However, certain related results from neurocomputing theory are quite practical and signify that there exists some scope for neurocomputing in multi-criteria decision analysis.