The classical First and Second Borel-Cantelli theorems as well as the
Kolmogorov Zero-One Laws have been extended to the abstract setting of
Riesz spaces by Wen-Chi Kuo, Coenraad C. A. Labuschagne and Bruce A.
Watson. This dissertation aims to extend upon the work of these authors. In
particular, an extension of the Barndorff-Nielsen Zero-One Law to the Riesz
space setting.
