Kuratowski and Ryll-Nardzewski measurable selection theorem

The Kuratowski and Ryll-Nardzewski measurable selection theorem[1][2][3] states that a weakly measurable correspondence with nonempty closed values from a measurable space into a Polish space admits a measurable selector. It is widely used in mathematical economics and optimal control.[4]

See also

References

  1. ↑ Aliprantis; Border (2006). Infinite-dimensional analysis. A hitchhiker's guide.
  2. ↑ Kechris, Alexander S. (1995). Classical descriptive set theory. Springer-Verlag. Theorem (12.13) on page 76.
  3. ↑ Srivastava, S.M. (1998). A course on Borel sets. Springer-Verlag. Sect. 5.2 "Kuratowski and Ryll-Nardzewski’s theorem".
  4. ↑ Cascales, Bernardo; Kadets, Vladimir; Rodríguez, José (2010). "Measurability and Selections of Multi-Functions in Banach Spaces" (PDF). Journal of Convex Analysis 17 (1): 229–240. Retrieved 7 April 2015.
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