Abstract

We show that an exact version of Fatou's lemma for Gelfand integrable functions can be obtained by combining Young measure techniques and results due to E. J. Balder [New fundamentals of Young measure convergence, in: S. Reich, A. Ioffe and I. Shafrir (eds.), Calculus of Variations and Optimal Control, Chapman and Hall 2000, 24–48; and A Fatou lemma for Gelfand integrals by means of Young measure theory, Positivity 6 (2002) 317–329] with a purification result of M. Greinecker and K. Podczeck [Purification and roulette wheels, Economic Theory 58 (2015) 255–272].

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Keywords

  • Gelfand integral
  • Fatou's lemma
  • purification

Mathematics Subject Classification

28B05, 28B20; 46G10

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Suggested citation

M. Greinecker, K. Podczeck. “An Exact Fatou's Lemma for Gelfand Integrals by Means of Young Measure Theory.” Journal of Convex Analysis 24 (2017), No. 2, 621–644. https://doi.org/10.68381/jca24039

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Published by Heldermann Verlag, 2017. Rights now held by Banach Press LLC.