Compatible measures and merging

Ehud Lehrer, Rann Smorodinsky

Research output: Contribution to journalArticlepeer-review


Two measures, μ and μ, are updated as more information arrives. If with μ-probability 1, the predictions of future events according to both measures become close, as time passes, we say that μ merges to μ. Blackwell and Dubins (1962) showed that if μ is absolutely continuous with respect to μ then μ merges to μ. Restricting the definition to prediction of near future events and to a full sequence of times yields the new notion of almost weak merging (AWM), presented here. We introduce a necessary and sufficient condition and show many cases with no absolute continuity that exhibit AWM. We show, for instance, that the fact that μ is diffused around μ implies AWM.

Original languageEnglish
Pages (from-to)697-706
Number of pages10
JournalMathematics of Operations Research
Issue number3
StatePublished - Aug 1996


  • Almost weak merging
  • Merging of opinions
  • Strong law of large numbers


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