Martingale Transforms of the Rademacher Sequence in Symmetric Spaces

Sergey V. Astashkin
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Sergey V. Astashkin: Samara National Research University

Chapter Chapter 13 in The Rademacher System in Function Spaces, 2020, pp 419-438 from Springer

Abstract: Abstract Let { A k } k = 0 ∞ $$\{\mathcal {A}_k\}_{k=0}^\infty $$ be a filtration of σ-algebras on a probability space ( Ω , A , ℙ ) $$(\Omega ,\mathcal {A},\mathbb {P})$$ , i.e., A 0 ⊂ 1 ⊂ ⋯ ⊂ A k ⊂ ⋯ ⊂ A . $$\mathcal {A}_0\subset \mathcal { A}_1\subset \dots \subset \mathcal {A}_k\subset \dots \subset \mathcal {A}.$$ A sequence of random variables (r.v.’s) { v k } k = 1 ∞ $$\{v_k\}_{k=1}^\infty $$ is said to be predictable with respect to this filtration (or { A k } $$\{\mathcal {A}_k\}$$ -predictable) if v k is A k − 1 $$\mathcal {A}_{k-1}$$ -measurable for every k = 1, 2, ….

Date: 2020
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DOI: 10.1007/978-3-030-47890-2_13

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