{"status":"ok","message-type":"work","message-version":"1.0.0","message":{"indexed":{"date-parts":[[2025,10,10]],"date-time":"2025-10-10T00:52:20Z","timestamp":1760057540478,"version":"build-2065373602"},"reference-count":33,"publisher":"MDPI AG","issue":"2","license":[{"start":{"date-parts":[[2025,2,14]],"date-time":"2025-02-14T00:00:00Z","timestamp":1739491200000},"content-version":"vor","delay-in-days":0,"URL":"https:\/\/creativecommons.org\/licenses\/by\/4.0\/"}],"content-domain":{"domain":[],"crossmark-restriction":false},"short-container-title":["Axioms"],"abstract":"<jats:p>We obtain a new extended description of the exceptional set in the asymptotic Borel-type relation in terms of the maximum of the integrand function for the Laplace\u2013Stieltjes integrals. The obtained description of an exceptional set in the Borel-type relation leaves no room for improvement. In particular, we construct a corresponding measure, a function given by the Laplace\u2013Stieltjes integral with respect to this measure, and a measurable set for which the opposite inequality to the Borel-type relation is fulfilled.<\/jats:p>","DOI":"10.3390\/axioms14020134","type":"journal-article","created":{"date-parts":[[2025,2,14]],"date-time":"2025-02-14T04:48:51Z","timestamp":1739508531000},"page":"134","update-policy":"https:\/\/doi.org\/10.3390\/mdpi_crossmark_policy","source":"Crossref","is-referenced-by-count":0,"title":["On the New Description of Exceptional Sets in Asymptotic Estimates for the Entire Functions and the Laplace\u2013Stieltjes Integrals"],"prefix":"10.3390","volume":"14","author":[{"ORCID":"https:\/\/orcid.org\/0000-0001-5217-8394","authenticated-orcid":false,"given":"Oleh","family":"Skaskiv","sequence":"first","affiliation":[{"name":"Faculty of Mechanics and Mathematics, Ivan Franko National University of Lviv, 79000 Lviv, Ukraine"}]},{"ORCID":"https:\/\/orcid.org\/0000-0003-0598-2237","authenticated-orcid":false,"given":"Andriy","family":"Bandura","sequence":"additional","affiliation":[{"name":"Department of Physics and Mathematics, Ivano-Frankivsk National Technical University of Oil and Gas, 76019 Ivano-Frankivsk, Ukraine"}]},{"ORCID":"https:\/\/orcid.org\/0000-0001-9469-7459","authenticated-orcid":false,"given":"Tetyana","family":"Salo","sequence":"additional","affiliation":[{"name":"Department of Mathematics, Lviv Polytechnic National University, 79000 Lviv, Ukraine"}]},{"ORCID":"https:\/\/orcid.org\/0000-0002-5066-3692","authenticated-orcid":false,"given":"Dmytro","family":"Zikrach","sequence":"additional","affiliation":[{"name":"Softserve, Inc., 79021 Lviv, Ukraine"}]}],"member":"1968","published-online":{"date-parts":[[2025,2,14]]},"reference":[{"key":"ref_1","doi-asserted-by":"crossref","first-page":"142","DOI":"10.1007\/BF01077275","article-title":"A Tauberian theorem for the Laplace-Stieltjes integrals","volume":"20","author":"Krainova","year":"1986","journal-title":"Funct. 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