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Paper IPM / M / 8736  


Abstract:  
A pair (X, N) is said to be a probabilistic normed space if X
is a real vector space, N is a mapping from X into the set of
all distribution functions (for x ∈ X, the distribution
function N(x) is denoted by N_{x}, and N_{x}(t) is the value
N_{x}, at t ∈ \mathbbR satisfying the following
conditions:
(NI) N_{x}(0) = 0, (N2) N_{x}(t) = 1 for all t > 0 iff x = 0, (N3) N_{ax}(t) = N_{x}([(t)/(α)]) for all α ∈ \mathbbR\{0}, (N4) N_{x+y}(s + t) ≥ min{N_{x}(s), N_{y}(t)} for all x, y ∈ X, and s,t ∈ \mathbbR_{0}^{+} Download TeX format 

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