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Abstract

The goals of this chapter are to: • Extend the notion of uniformity, • Study the metrization of weak convergence, • Describe the notion of vague convergence, • Consider the question of its metrization.

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Notes

  1. 1.

    See Definition 4.4.1 in Chap. 4.

  2. 2.

    See, for example, Hennequin and Tortrat [1965].

  3. 3.

    See (8.3.5)–(8.3.7) in Chap. 8.

  4. 4.

    See Billingsley (1999, Sect. 5).

  5. 5.

    See Kallenberg [1975] and Kerstan et al. [1978].

  6. 6.

    See Kallenberg [1975], Szasz [1975], and Kerstan et al. [1978].

  7. 7.

    See Example 3.3.2 in Chap. 3.

References

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Rachev, S.T., Klebanov, L.B., Stoyanov, S.V., Fabozzi, F.J. (2013). Uniformity in Weak and Vague Convergence. In: The Methods of Distances in the Theory of Probability and Statistics. Springer, New York, NY. https://doi.org/10.1007/978-1-4614-4869-3_11

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