  This appendix proves CORN's universal consistency. One of Bin's PhD thesis
examiner (Special thanks to Vladimir Vovk from Royal Holloway, University of
London) suggested that CORN is universal and provided sketch proof of Lemma
1.6, which is the key of this proof. Based on the proof in Gy\"prfi et al.
[2006], we thus prove CORN's universal consistency. Note that the notations in
this appendix follows Gy\"orfi et al. [2006].
