Nonexistence of measurable optimal selections

John Burgess, Ashok Maitra

Research output: Contribution to journalArticlepeer-review

2 Scopus citations


We give an example of a function f on a separable metric space X into a compact metric space Y such that the graph of f is a Borel subset of X × Y, but f is not Borel measurable. The example forms the basis for our construction of an upper semicontinuous, compact model of a one-day dynamic programming problem where the player has an optimal action at each state, but is unable to make a choice of such an action in a Borel measurable manner.

Original languageEnglish (US)
Pages (from-to)1101-1106
Number of pages6
JournalProceedings of the American Mathematical Society
Issue number4
StatePublished - Dec 1992

All Science Journal Classification (ASJC) codes

  • General Mathematics
  • Applied Mathematics


  • Borel sets and functions
  • Dynamic programming
  • Measurable selections


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