Abstract
Contents Introduction §1. The strong law of large numbers of Borel and its refinements §2. The Khintchine inequalities §3. Martingale extensions of the Khintchine inequalities. 1. Preliminary consideration §4. Martingale extensions of the Khintchine inequalities. 2. The Burkholder inequalities for §5. The maximal Khintchine inequalities §6. The martingale extension of maximal Khintchine inequalities. (The inequalities of Davis for and of Burkholder and Davis for ) §7. Comparison inequalities for martingale transforms §8. On the best constants in the Khintchine inequalities §9. The Khintchine inequalities in (exponential) Orlicz spaces §10. On the best constants in the Burkholder inequalities () §11. Some refinements of the Khintchine inequalities (the Whittle inequalities, the Rosenthal inequalities, and their modifications and extensions to the martingale case)
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