Abstract
This chapter discusses the kinds of convergence of a measure sequence most frequently met in classical analysis. The typical context to be considered is the following. A class M of measures on a measurable space (S, S) is given, together with a class Γ of functions from S into R. The problem is to find a definition of convergence of the sequence λ∂ in M to a measure λ in M, which implies that limλ∂[f] = λ[f] for every function f in Γ. This problem has an easy solution, a solution by definition: the sequence λ∂ is Γ convergent to λ if
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© 1994 Springer Science+Business Media New York
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Doob, J.L. (1994). Convergence of Measure Sequences. In: Measure Theory. Graduate Texts in Mathematics, vol 143. Springer, New York, NY. https://doi.org/10.1007/978-1-4612-0877-8_9
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DOI: https://doi.org/10.1007/978-1-4612-0877-8_9
Publisher Name: Springer, New York, NY
Print ISBN: 978-1-4612-6931-1
Online ISBN: 978-1-4612-0877-8
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