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math.PR2008★ 1 cited
Optimal L-bounds for submartingales
Lutz Mattner, Uwe Rösler
The optimal function satisfying $$ \mathbb{E} |\sum_{1}^n X_i | \ge f(\mathrbb{E}|X_1|,...,\mathbb{E}|X_n|) $$ for every martingale is sho…
math.CA2008★ 2 cited
Sums of norm spheres are norm shells and lower triangle inequalities are sharp
Lutz Mattner
The statements in the title are explained and proved, as a little exercise in elementary normed vector space theory at the level of Chapter 5 of Dieudonné's "Foundations of Mathema…