Abctract:

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].

Keywords: Gelfand integral, Fatou's lemma, purification.