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| Paper IPM / M / 8736 |
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| Abstract: | |
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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 Nx, and Nx(t) is the value
Nx, at t ∈ \mathbbR satisfying the following
conditions:
(NI) Nx(0) = 0, (N2) Nx(t) = 1 for all t > 0 iff x = 0, (N3) Nax(t) = Nx([(t)/(|α|)]) for all α ∈ \mathbbR\{0}, (N4) Nx+y(s + t) ≥ min{Nx(s), Ny(t)} for all x, y ∈ X, and s,t ∈ \mathbbR0+ Download TeX format |
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