Geodesic
One-sided Dirac measures and the game with a discontinuous payoff function
Izvestiya Instituta Matematiki i Informatiki Udmurtskogo Gosudarstvennogo Universiteta, Tome 36 (2006) no. 2, pp. 65-68.

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We construct a space of measures where the consideration of the measures with discontinuous densities is possible. As is shown, consideration of certain games with discontinuous payoff functions in the constructed space of measures allows us to provide an existence of Nash equilibria. 
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     author = {D. M. Kinzebulatov},
     title = {One-sided {Dirac} measures and the game with a discontinuous payoff function},
     journal = {Izvestiya Instituta Matematiki i Informatiki Udmurtskogo Gosudarstvennogo Universiteta},
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D. M. Kinzebulatov. One-sided Dirac measures and the game with a discontinuous payoff function. Izvestiya Instituta Matematiki i Informatiki Udmurtskogo Gosudarstvennogo Universiteta, Tome 36 (2006) no. 2, pp. 65-68. http://geodesic.mathdoc.fr/item/IIMI_2006_36_2_a14/

[1] Derr V. Ya., Kinzebulatov D. M., “Obobschennye funktsii s razryvnymi osnovnymi funktsiyami i lineinye differentsialnye uravneniya”, Vestn. Udm. un-ta, 2005, no. 1, 35–58

[2] Derr V. Ya., Kinzebulatov D. M., “Alfa-integral tipa Stiltesa”, Vestn. Udm. un-ta, 2006, no. 1, 41–62