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# Averaging Operators and Martingale Inequalities in Rearrangement Invariant Function Spaces

 MSC Classifications: 60G44 - Martingales with continuous parameter 60G46 - Martingales and classical analysis 46E30 - Spaces of measurable functions ($L^p$-spaces, Orlicz spaces, Kothe function spaces, Lorentz spaces, rearrangement invariant spaces, ideal spaces, etc.)