TY - JOUR AU - Buczolich, Zoltán TI - Almost Everywhere Convergence Questions of Series of Translates of Non-Negative Functions JF - REAL ANALYSIS EXCHANGE J2 - REAL ANALYSIS EXCHANGE VL - 48 PY - 2023 IS - 1 SP - 49 EP - 76 PG - 28 SN - 0147-1937 DO - 10.14321/realanalexch.48.1.1663223339 UR - https://m2.mtmt.hu/api/publication/33755338 ID - 33755338 N1 - Export Date: 9 May 2023 Correspondence Address: Buczolich, Z.; Department of Analysis, Pázmány Péter Sétány 1/c, Hungary; email: zoltan.buczolich@ttk.elte.hu Funding details: Horizon 2020 Framework Programme, H2020, 741420 Funding details: European Research Council, ERC Funding details: Nemzeti Kutatási Fejlesztési és Innovációs Hivatal, NKFIH, 124003 Funding text 1: 60F20Key words: almost everywhere convergence, asymptotically dense sets, Borel–Cantelli lemma, laws of large numbers, zero-one laws Received by the editors September 15, 2022 Communicated by: Paul D. Humke ∗The project leading to this application has received funding from the European Research Council (ERC) under the European Union’s Horizon 2020 research and innovation programme (grant agreement No. 741420). This author was also supported by the Hungarian National Research, Development and Innovation Office–NKFIH, Grant 124003 and at the time of part of the work on this paper was holding a visiting researcher position at the Rényi Institute. LA - English DB - MTMT ER - TY - JOUR AU - Buczolich, Zoltán AU - Hanson, B. AU - Maga, Balázs AU - Vértesy, Gáspár TI - Type 1 and 2 sets for series of translates of functions JF - ACTA MATHEMATICA HUNGARICA J2 - ACTA MATH HUNG VL - 158 PY - 2019 IS - 2 SP - 271 EP - 293 PG - 23 SN - 0236-5294 DO - 10.1007/s10474-019-00937-2 UR - https://m2.mtmt.hu/api/publication/30767541 ID - 30767541 N1 - Department of Analysis, ELTE Eötvös Loránd University, Pázmány Péter Sétány 1/c, Budapest, 1117, Hungary Department of Mathematics, Statistics and Computer Science, St. Olaf College, Northfield, MN 55057, United States Export Date: 19 September 2019 Correspondence Address: Buczolich, Z.; Department of Analysis, ELTE Eötvös Loránd University, Pázmány Péter Sétány 1/c, Hungary; email: buczo@cs.elte.hu Funding text 1: Z. Buczolich thanks the R?nyi Institute where he was a visiting researcher for the academic year 2017-18. B. Hanson would like to thank the Fulbright Commission, the Budapest Semesters in Mathematics, and the R?nyi Institute for their generous support during the Spring of 2018, while he was visiting Budapest as a Fulbright scholar. AB - Suppose Lambda is a discrete infinite set of nonnegative real numbers. We say that Lambda is type 1 if the series s(x)=Sigma lambda is an element of Lambda f(x+lambda) satisfies a zero-one law. This means that for any non-negative measurable f:R ->[0,+infinity) either the convergence set C(f,Lambda)={x:s(x)<+infinity}=R modulo sets of Lebesgue zero, or its complement the divergence set D(f,Lambda)={x:s(x)=+infinity}=R modulo sets of measure zero. If Lambda is not type 1 we say that Lambda is type 2.The exact characterization of type 1 and type 2 sets is not known. In this paper we continue our study of the properties of type 1 and 2 sets. We discuss sub and supersets of type 1 and 2 sets and give a complete and simple characterization of a subclass of dyadic type 1 sets. We discuss the existence of type 1 sets containing infinitely many elements independent over the rationals. Finally, we consider unions and Minkowski sums of type 1 and 2 sets. LA - English DB - MTMT ER -