30 | 05 | 2024


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Article 51

Set-functions that are σ-finite whenever they are absolutely continuous


Mathematical reviews subject classification: 26A45, 26A46, 26A24.



The main result of this paper is Theorem 2.2, that establishes some necessary conditions for an increasing set-function in order to be σ-finite, or σ-null.

Then we give applications of this main result:

  • we find characterizations of the VBG, ACG, VB*G and AC*G functions (see Theorems 3.1 and 3.2);
  • we find characterizations of the VBnG and the ACnG functions (see Theorem 4.1);
  • for three special set-functions, we show that they are σ-finite, whenever they are absolutely continuous (see Theorem 5.1).


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