Exercise 2. Consider the function f: [0, 1] → R defined by O ifx e Q f(x) =- Vx ifx eR\Q Show in full detail that the function f: (i) is measurable, (ii) is not Riemann integrable, (ii) is Lebesgue integrable. Finally, calculate the value of where E = [0, 1].

Advanced Engineering Mathematics
10th Edition
ISBN:9780470458365
Author:Erwin Kreyszig
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Chapter2: Second-order Linear Odes
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Exercise 2. Consider the function f: [0, 1] → R defined by
0 ifx e Q
f(x) =-
Vx ifx eR\Q
Show in full detail that the function f:
(i) is measurable,
(ii) is not Riemann integrable,
(ii) is Lebesgue integrable.
Finally, calculate the value of
where E = [0, 1].
Transcribed Image Text:Exercise 2. Consider the function f: [0, 1] → R defined by 0 ifx e Q f(x) =- Vx ifx eR\Q Show in full detail that the function f: (i) is measurable, (ii) is not Riemann integrable, (ii) is Lebesgue integrable. Finally, calculate the value of where E = [0, 1].
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