An Exact Fatou's Lemma for Gelfand Integrals by Means of Young Measure Theory

Michael Greinecker; Konrad Podczeck

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].

Author information

Contact details are reproduced from the original publication and may be historical.

Michael Greinecker

Department of Economics, University of Graz, Universitätsstr. 15, 8010 Graz, Austria

michael.greinecker@uni-graz.at

Konrad Podczeck

Department of Economics, University of Vienna, Oskar-Morgenstern-Platz 1, 1090 Wien, Austria

konrad.podczeck@univie.ac.at

Keywords

Gelfand integral
Fatou's lemma
purification

Mathematics Subject Classification

28B05, 28B20; 46G10

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.