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In this paper we generalize the Hajek-Renyi-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… Click to show full abstract
In this paper we generalize the Hajek-Renyi-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 $1\le p\le 2$.
Keywords:
maximal inequality;
strong law;
chow maximal;
riesz spaces;
law large;
inequality
Journal Title: Journal of Mathematical Analysis and Applications
Year Published: 2020
Link to full text (if available)
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Journal Title: Journal of Mathematical Analysis and Applications
Year Published: 2020
Link to full text (if available)
Share on Social Media: Sign Up to like & get
recommendations!