Patterson, Richard F.Savaş, Ekrem2020-11-212020-11-2120090893-9659https://doi.org/10.1016/j.aml.2009.01.057https://hdl.handle.net/11467/3622The notion of asymptotically equivalent sequences was presented by Pobyvanets in 1980. Using this definition, he presented Silverman-Toeplitz-type matrix conditions that ensure that a summability matrix preserves asymptotic equivalency. This work begins with an extension of Pobyvanets' definition of convergence in probability. This definition is also used to present Silverman-Toeplitz-type conditions for ensuring that a summability matrix preserves asymptotic probability equivalence. In addition, we shall also present a Marouf-type characterization of such a sequence space. © 2009 Elsevier Ltd. All rights reserved.eninfo:eu-repo/semantics/openAccessAsymptoticallyEquivalent sequencesRegular matrixArticle221014911495Q2WOS:000270057200002Q12-s2.0-6834912365810.1016/j.aml.2009.01.057