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We study such characterizations based on the asymptotic density of positive answers. In particular, this note provides a new learning-theoretic definition of weak 2-randomness, solving the problem posed by (Zaffora Blando, Rev. Symb. Log. 2019). The note also highlights the close connection between these characterizations and the problem of convergence on random sequences.<\/jats:p>","DOI":"10.1017\/s1755020321000125","type":"journal-article","created":{"date-parts":[[2021,3,22]],"date-time":"2021-03-22T07:18:16Z","timestamp":1616397496000},"page":"807-822","update-policy":"http:\/\/dx.doi.org\/10.1017\/policypage","source":"Crossref","is-referenced-by-count":0,"title":["A NOTE ON THE LEARNING-THEORETIC CHARACTERIZATIONS OF RANDOMNESS AND CONVERGENCE"],"prefix":"10.1017","volume":"15","author":[{"given":"TOMASZ","family":"STEIFER","sequence":"first","affiliation":[]}],"member":"56","published-online":{"date-parts":[[2021,3,22]]},"reference":[{"key":"S1755020321000125_r19","doi-asserted-by":"publisher","DOI":"10.1090\/S0002-9939-2013-11710-7"},{"key":"S1755020321000125_r15","doi-asserted-by":"publisher","DOI":"10.1016\/S0019-9958(66)80018-9"},{"key":"S1755020321000125_r6","doi-asserted-by":"publisher","DOI":"10.1214\/aoms\/1177706899"},{"key":"S1755020321000125_r2","unstructured":"[2] Bailey, D. 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(2020). Universal coding and prediction on Martin-L\u00f6f ergodic random points. Preprint, arXiv:2005.03627."},{"key":"S1755020321000125_r16","doi-asserted-by":"crossref","unstructured":"[16] Milovanov, A. (2020). Predictions and algorithmic statistics for infinite sequence. 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