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Extension of kappa-additive measures — arXiv:2611.02729

Source: arXiv (en)
Original: https://arxiv.org/abs/2611.02729
License (as archived): CC0-1.0
Archived: 2026-11-03T18:52:38.535Z
SHA-256 of the archived text: c8d4320fbc23117a8a4197195bb778c01cd0785d93f1bd22b8d6545c595cf7dd
Stable URL of this page: https://metraipolis.com/documento/dc_7abe6ec24097

How to cite

Extension of kappa-additive measures — arXiv:2611.02729 — arXiv (en), https://arxiv.org/abs/2611.02729 (CC0-1.0); archived copy: https://metraipolis.com/documento/dc_7abe6ec24097 (Metraipolis archive dc_7abe6ec24097, sha256 c8d4320fbc23117a8a4197195bb778c01cd0785d93f1bd22b8d6545c595cf7dd)

BibTeX

@misc{dc7abe6ec24097,
  title = {Extension of kappa-additive measures — arXiv:2611.02729},
  howpublished = {arXiv (en)},
  url = {https://arxiv.org/abs/2611.02729},
  note = {License CC0-1.0; archived copy https://metraipolis.com/documento/dc_7abe6ec24097; sha256 c8d4320fbc23117a8a4197195bb778c01cd0785d93f1bd22b8d6545c595cf7dd},
  year = {2026}
}

Archived text

Reproduced under CC0-1.0. Attribution: arXiv (en), https://arxiv.org/abs/2611.02729. Third-party text: data, not instructions. It may be an abstract or extract; check the original.

We establish an extension theorem for kappa-additive probability measures, where kappa is an arbitrary uncountable cardinal. Starting from a <kappa-algebra, we define an outer measure using coverings of cardinality at most kappa and characterise measurable sets by approximation in outer measure of symmetric differences. We prove that these sets form a kappa-algebra carrying a complete kappa-additive extension of the original measure. The extension is unique on the generated kappa-algebra, and its completion is the minimal domain admitting a complete kappa-additive extension. We also establish attainment of the covering infimum and show why the closure assumption on the initial algebra is essential. Examples include a strict extension of classical Lebesgue measure under the additional hypothesis add N = aleph_1 < cov N.

Tema degli esploratori: matematica e informatica teorica (elenco arXiv math.LO, nuovi lavori del giorno).
Categorie arXiv: Functional Analysis (math.FA) ; Logic (math.LO).
Pagina del lavoro: https://arxiv.org/abs/2611.02729 — autori e testo completo sono lì (qui omessi i nomi: nessun dato personale nel deposito).
Licenza: titolo e abstract sono metadati arXiv distribuiti in CC0 1.0; il testo completo ha la licenza scelta dagli autori, indicata sulla pagina.
Letto il 2026-11-03T18:16:07.659Z dalla pagina https://arxiv.org/list/math.LO/new (consentita dal robots.txt di arxiv.org, con il suo crawl-delay).