Positivity

, Volume 22, Issue 1, pp 139–140 | Cite as

Correction to: Measures under the flat norm as ordered normed vector space

  • Piotr Gwiazda
  • Anna Marciniak-Czochra
  • Horst R. Thieme
Correction
  • 120 Downloads

1 Correction to: Positivity DOI 10.1007/s11117-017-0503-z

Corollary 4.16 needs to be restated as

Corollary 4.16

\(\mathcal{M}_+^s(S)\) is a cone of \(\mathcal{M}(S)\).

\(\mathcal{M}_+^t(S)\) is a cone of \(\mathcal{M}(S)\) if S is complete, because then \(\mathcal{M}_+^t(S) = M_+^s(S)\). In general, \(\mathcal{M}_+^t(S)\) is not a cone of \(\mathcal{M}(S)\) because it is not closed.

It follows from Remark 4.20 that \(\mathcal{M}_+^t(S)\) is dense in \(\mathcal{M}_+^s(S)\). Assume that \(\mathcal{M}_+^t(S)\) is closed and S is separable. Then, \(\mathcal{M}_+^t(S) = \mathcal{M}_+(S)\). This implies that S is universally measurable; however, not all separable metric spaces are universally measurable ([1, Sect. 11.5]).

Reference

  1. 1.
    Dudley, R.M.: Real Analysis and Probability, 2nd edn. Cambridge University Press, Cambridge (2002)CrossRefMATHGoogle Scholar

Copyright information

© Springer International Publishing AG 2017

Authors and Affiliations

  • Piotr Gwiazda
    • 1
  • Anna Marciniak-Czochra
    • 2
  • Horst R. Thieme
    • 3
  1. 1.Institute of Applied Mathematics and MechanicsUniversity of WarsawWarszawaPoland
  2. 2.Institute of Applied MathematicsUniversity of HeidelbergHeidelbergGermany
  3. 3.School of Mathematical and Statistical SciencesArizona State UniversityTempeUSA

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