2021/11/30 by Karatzas, Ioannis, Schachermayer, Walter · 1 citation
#60A10 #60F15 #FOS: Mathematics #Probability (math.PR)
paper · doi:10.48550/arxiv.2111.15469
In the spirit of the famous KOMLÓS (1967) theorem, every sequence of nonnegative, measurable functions \ fn \n ∈ \N on a probability space, contains a subsequence which - along with all its subsequences - converges a.e. in CESÀRO mean to some measurable f_* : Ω→ [0, ∞]. This result of VON WEIZSÄCKER (2004) is proved here using a new methodology and elementary tools; these sharpen also a theorem of DELBAEN & SCHACHERMAYER (1994), replacing general convex combinations by CESÀRO means.