• Corpus ID: 249097803

Vague and weak convergence of signed measures

  title={Vague and weak convergence of signed measures},
  author={Martin Herdegen and Gechun Liang and Osian Shelley},
Necessary and sufficient conditions for weak and vague convergence of measures are important for a diverse host of applications. This paper aims to give a comprehensive description of the relationship between the two modes of convergence when the measures are signed, which is largely absent from the literature. Furthermore, when the underlying space is R , we study the relationship between vague convergence of signed measures and the pointwise convergence of their distribution functions. 

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An Introduction to Probability Theory and Its Applications, Volume 2, 2nd Edition

  • 1971

Measure Theory, Springer-Verlag, Berlin Heidelberg, 2007 (en)

  • 2007

On Tauberuan Theorem for Generalised Signed Measures, Working paper (2022)

  • 2022

Planinić, A note on vague convergence of measures, Statistics & Probability Letters

  • 2019

Foundations of modern probability, second edition ed., Probability and its

  • 2002