Introduction The mathematical theor y o f differentia l game s is presented i n Friedman' s boo k [20 ] which appeared i n 1971 . I n this book th e fundamenta l concept s o f value, strategy, saddl e point, etc. are defined , an d th e basi c existence theor y i s developed. Th e connectio n wit h the Hamilton-Jacob i equation s i s also described . The presen t surve y i s based on th e abov e mentione d boo k an d o n som e more recen t work, mainly b y Elliot t an d Kalto n ([5]-[8] ) an d b y Friedma n ([21]-[27]). The papers that ar e quoted i n th e surve y appea r i n th e Bibliography . Othe r recen t papers in differential game s appear i n the Supplementar y Bibliography . Fo r th e earlie r litera - ture, see [20] . Finally, all the function s i n thi s work ar e rea l valued. This wor k wa s partiall y supporte d b y Nationa l Scienc e Foundatio n gran t GP-3 5 347X . 1 http://dx.doi.org/10.1090/cbms/018/01

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