Relative redundancy for large alphabets

Standard redundancy measures the excess number of bits required to encode a sequence of a given length when the underlying distribution is not known. Relative redundancy measures the same increase, but as a function of the sequence´s minimum description length. We consider the relative redundancy of i.i.d. distributions over large alphabets and show that, like standard redundancy, relative redundancy too increases with the alphabet size. We then consider compression of patterns of i.i.d. strings. Again analogous to standard redundancy, we show that the relative redundancy of patterns of large, or even infinite alphabet i.i.d. distributions is negligible compared to the patterns´ minimum description length