University of Qom Measure Algebras and Applications 3116-014X 1 1 2023 09 23 On Rado's theorem and its related problems مقدمه‌ای بر قضیه رادو و مسائل مرتبط 83 96 2525 10.22091/maa.2023.9445.1002 EN Mahmoud Mohammadzadeh Jafarabadi Department of Mathematics, University of Guilan, Rasht, Guilan, Iran Mohammad Akbari Tootkaboni Department of Mathematics, University of Guilan, Rasht, Guilan, Iran 0000-0002-4183-8817 Journal Article 2023 05 15 In this paper, we state Rado's theorem, Ramsey families, and their connections with ergodic theory and combinatorial problems. We discuss the historical development of these concepts since their inception to how some problems in the fields of combinatorics and number theory were formulated and solved, particularly through the lens of dynamical systems. We also address some open questions in this field. Rado's theorem partition regular Ramsey theory Stone-Cech compactification upper density https://maa.qom.ac.ir/article_2525_6d81a0bc74c180e464c181466181e00d.pdf