On some properties of Lévy vectors and their variations

Abstract We investigate some properties of Lévy vectors vector series Σ n ∈ ω v . consider a generalization an example from [P. Klinga, Rearranging on small set, J. Math. Anal. Appl. , 424(2):966–974, 2015] proving that for special class series, there exists subseries has no convergent with the sum range equal to plane. To prove this result, we introduce useful notion supervector and its properties.