Vitali?Hahn?Saks theorem

In mathematics, the Vitali?Hahn?Saks theorem states that given μn for each integer n >0, a countably additive function defined on a fixed sigma-algebra Σ, with values in a given Banach space B, such that

Related Topics:
Mathematics - Countably additive function - Sigma-algebra - Banach space

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:lim_{n ightarrow infty} mu_n(X) ightarrow mu(X)

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exists for every set X in Σ, then μ is also countably additive. In other words, the limit of a sequence of spectral measures is a spectral measure.

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