Continuity and Outer Measure - Let f(x) be a positive continuous function on [0,1/2], f(x) =< 1/2.
Let A = { (x,y) : 0 =< x = 1/2, 0=
Continuity of a Max Function on [0,1] X [0,1] - Let f(x,y) be a real valued continuous function defined on the unit square [0,1] X [0,1].
Prove g(x)=max{f(x,y) : y in [0,1]} is continuous.
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Can we treat g(x) as a composite function that ...