LetXand Y be nonemptysetsandleth : X x Y --+JRhaveboundedrangeinR Let F: X --+ JR andG
Chapter 2, Problem 11(choose chapter or problem)
LetXand Y be nonemptysetsandleth : X x Y --+JRhaveboundedrangeinR Let F: X --+ JR andG : Y --+ JRbe definedby F(x) := sup{h(x, y) : y e Y}, G(y) := sup{h(x, y) : x eX}. Establish the Principle of the Iterated Suprema: sup{h(x, y) : x eX, y e Y} = sup{F(x) : x eX} = sup{G(y) : y e Y} We sometimes express this in symbols by suph(x, y) = supsuph(x, y) = supsuph(x, y). x,y x y y x 1
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