Author/Authors :
Sastry، K.P.R. نويسنده Visakhapatnam,India , , Naidu، G.A. نويسنده Department of Mathematics,Andhra University,Visakhapatnam,India , , Latha، V. Madhavi نويسنده Department of Mathematics,Andhra University,Visakhapatnam,India , , Sastri، S.S.A. نويسنده Department of Mathematics,G.V.P. College of Engineering,Visakhapatnam,India , , Gayatri، I. Laxmi نويسنده Department of Engg. Mathematics,GITAM University,Visakhapatnam,India ,
Abstract :
In this paper, we study Menger Probabilistic Normed (PN) spaces in a detailed way; we introduce the notation of a finite product of Menger Probabilistic Normed spaces, show that a finite product of complete Menger probabilistic normed spaces is itself complete and every Cauchy sequence in a Menger probabilistic normed space is norm totally bounded under certain conditions. We also introduce the notion of L-Menger PN spaces and show that in a L-Menger PN space (X, \tilde{F}, *), the distribution map \tilde{F} determines and is determined by a single distribution function on R.
Keywords :
Menger spaces , Probabilistic metric space , Menger probabilistic normed space , L-Menger
probabilistic normed space ,
