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In this paper we consider the maps which preserve a relative probability measure on a set M. We prove that a mapping g : M → M preserves a relative probability measure 
if and only if 
, for each simple function 
. We also prove that g preserves for each observer 
, if and only if g has a fixed point. We show that if there is x in M such that
for each 
, then there is a mapping f : M → M such that g preserves .
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