Prove: By taking the following problem as being given/true : (Analysis on Metric Spaces) Let f...

Question

Question

Prove:

Let f : [0, 1] x [0, 1] + R be defined by f(x,y) = ſi if y=x? if y #r? Show that f is integrable on [0, 1] x [0,1].

By taking the following problem as being given/true :

Let f : [0, 1] + R be uniformly continuous, so that for every e > 0, there exists 8 >0 such that -y<= f(x) - f(y)< € for ever

(Analysis on Metric Spaces)

Answer 1

Answer #1

1 2 • y=x² y 7x² by where 9:[0, BR g(x) = x² 1 y=x neighbour of (xo, ao contains points (x, y) & Gg Now consider gi[, ~ R by

Answer 2

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