The key theorem of learning theory on gλ measure spaces

Statistical learning theory or SLT which was introduced by Vladimir N. Vapnik, is a small sample statistics, which concerns mainly with the statistic principles when samples are limited, especially the properties of learning procedure in such cases. The key theorem of learning theory plays an important role in SLT, which is the foundation for the subsequent theories and applications. However, this theory only suits to a fixed probability measure, which reduces the application range of the theorem. Thus, we generalize the application range by means of changing the probability space into g_λ measure space.