Abstract
The convergence of an infinite series \(\sum _{n=1}^\infty X_n\) is a tail event.
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Notes
- 1.
Theorem 8.6 is a stronger statement than Kolmogorov’s classical strong law. It is due to Marcinkiewicz and Zygmund (1937) : Sur les fonctions indépendentes, Fund. Math. 29, 60–90., but clearly contains the classical law as a special case.
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Bhattacharya, R., Waymire, E.C. (2016). Random Series of Independent Summands. In: A Basic Course in Probability Theory. Universitext. Springer, Cham. https://doi.org/10.1007/978-3-319-47974-3_8
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DOI: https://doi.org/10.1007/978-3-319-47974-3_8
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