... of Sciences of the United States of America, vol. 27, pp. 222–224, 1941.5 T. Aoki, “On the stability of the linear transformation in Banach spaces,” Journal of the MathematicalSociety of Japan, vol. ... →∞μxntμxt.Proof. The proof is the same as classical random normed spaces, see 54.Journal of Inequalities and Applications 15Proof. The proof follows from Theorem 3.5 by takingΦx,yt:tt ... holds. The rest of the proof is similar to the proof of Theorem 3.1.Corollary 3.6. Let θ ≥ 0,andletp be a real number with p>1.LetX be a normed vector space withnorm ·,andletX, μ, T∧ be an...