We generalize McDiarmid's inequality for functions with bounded differences on a high probability set, using an extension argument. Those functions concentrate around their conditional expectations. We further extend the results to concentration in general metric spaces.

翻译：我们通过延拓论证，将McDiarmid不等式推广至在高概率集上具有有界差分的函数。这类函数在其条件期望附近呈集中现象。我们进一步将结果推广至一般度量空间中的集中现象。