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Semicontinuous integrands as jointly measurable maps

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  • Oriol Carbonell-Nicolau

    () (Rutgers University)

Abstract

Suppose that (X,A) is a measurable space and Y is a metrizable, Souslin space. Let Au denote the universal completion of A. Given f : X x Y !R and x 2 X, let f (x,¢) be the lower semicontinuous hull of f (x,¢). If f is (Au ­B(Y),B(R))-measurable, then f is (Au ­B(Y),B(R))-measurable.

Suggested Citation

  • Oriol Carbonell-Nicolau, 2015. "Semicontinuous integrands as jointly measurable maps," Departmental Working Papers 201512, Rutgers University, Department of Economics.
  • Handle: RePEc:rut:rutres:201512
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    File URL: http://www.sas.rutgers.edu/virtual/snde/wp/2015-12.pdf
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    1. Oriol Carbonell-Nicolau & Richard McLean, 2014. "On the existence of Nash equilibrium in Bayesian games," Departmental Working Papers 201402, Rutgers University, Department of Economics.
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    Cited by:

    1. Oriol Carbonell-Nicolau, 2017. "Perfect Equilibria in Games of Incomplete Information," Departmental Working Papers 201703, Rutgers University, Department of Economics.
    2. Oriol Carbonell-Nicolau & Richard McLean, 2014. "On the existence of Nash equilibrium in Bayesian games," Departmental Working Papers 201402, Rutgers University, Department of Economics.

    More about this item

    Keywords

    lower semicontinuous hull; jointly measurable function; measurable projection theorem; normal integrand;

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