The Hájek-Rényi-Chow maximal inequality and a strong law of large numbers in Riesz spaces

08/23/2019

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by   Wen-Chi Kuo, et al.

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In this paper we generalize the Hájek-Rényi-Chow maximal inequality for submartingales to L^p type Riesz spaces with conditional expectation operators. As applications we obtain a submartingale convergence theorem and a strong law of large numbers in Riesz spaces. Along the way we develop a Riesz space variant of the Clarkson's inequality for 1< p< 2.