Abstract
In this chapter we study the weak convergence of the distributions of sums of independent identically distributed random elements of a Banach space to a Gaussian distribution. First we consider type-2 operators whose relation to the CLT is established in Section 3.2. By means of this relation the CLT is proved in the spaces C(S) and c0, in particular.
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© 1989 Kluwer Academic Publishers
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Paulauskas, V., Račkauskas, A. (1989). The Central Limit Theorem in Banach Spaces. In: Approximation Theory in the Central Limit Theorem. Mathematics and Its Applications, vol 32. Springer, Dordrecht. https://doi.org/10.1007/978-94-011-7798-6_3
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DOI: https://doi.org/10.1007/978-94-011-7798-6_3
Publisher Name: Springer, Dordrecht
Print ISBN: 978-94-011-7800-6
Online ISBN: 978-94-011-7798-6
eBook Packages: Springer Book Archive