On Independence and Determination of Probability Measures

Iddo Ben-Ari ()
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Iddo Ben-Ari: University of Connecticut

Journal of Theoretical Probability, 2015, vol. 28, issue 3, 968-975

Abstract: Abstract We show that two probability measures defined on the same measure space having the same pairs of independent events are either purely atomic or equal. In the former case, either measures are trivial (taking values in $$\{0,1\}$$ { 0 , 1 } ) and singular, or equivalent. We also characterize nonatomic measures having the same events independent of a fixed (nontrivial) event and provide sufficient condition on pairs on independent intervals to determine a probability measure on the real line.

Keywords: Independence; Nonatomic; 60A99 (search for similar items in EconPapers)
Date: 2015
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DOI: 10.1007/s10959-013-0513-0

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