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Lebesgue decomposition type theorems for weakly null-additive functions on D-posets

  • Foundation, algebraic, and analytical methods in soft computing
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Abstract

In the present paper, we have developed the theory of weak null-additivity and absolute continuity in the realm of nonadditive measures on difference posets, and afterward proved two variants of the Lebesgue decomposition theorem in the context. A number of examples are constructed to illustrate the theory.

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Acknowledgements

The authors are grateful to the anonymous referees for their helpful suggestions for improving the paper.

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This research received no specific grant from any funding agency in the public, commercial, or not-for-profit sectors.

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Authors and Affiliations

  1. Department of Mathematics, University of Allahabad, Prayagraj, 211 002, India

    Mona Khare & Pratibha Pandey

  2. Department of Mathematics, C.M.P. Degree College, Prayagraj, 211 002, India

    Anurag Shukla

Authors
  1. Mona Khare
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  2. Anurag Shukla
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  3. Pratibha Pandey
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Correspondence to Pratibha Pandey.

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Khare, M., Shukla, A. & Pandey, P. Lebesgue decomposition type theorems for weakly null-additive functions on D-posets. Soft Comput 28, 3813–3821 (2024). https://doi.org/10.1007/s00500-023-09608-5

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