Suppose that E is a Jordan region and that f E R is integrable a) If f(E) H, for some compact set H, and H R is continuous, prove that o f is integrable on E b) Show that part a) is false if has even one point of discontinuity

Question: Suppose that E is a Jordan region and that f: E R is integrable. a) If f(E) H, for some compact set H,

Suppose that E is a Jordan region and that f: E → R is integrable.
a) If f(E) ⊂ H, for some compact set H, and ɸ : H → R is continuous, prove that ɸ o f is integrable on E.
b) Show that part a) is false if ɸ has even one point of discontinuity.

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