Function f with |f| is Lebesgue integrable but f isn't locally Lebesgue integrable

Stacie Worsley

Stacie Worsley

Answered

2022-01-15

Function f with |f| is Lebesgue integrable but f isn't locally Lebesgue integrable

Answer & Explanation

sonorous9n

sonorous9n

Expert

2022-01-16Added 34 answers

Step 1
In point of fact a function
f:RR
such that |f| is integrable will be integrable (locally and/or otherwise) if and only if it is measurable.
Your f is not measurable because
A=f1[12,),
and therefore it isn't integrable.
Beverly Smith

Beverly Smith

Expert

2022-01-17Added 42 answers

Step 1
Hint:
yXf(x)dx
=Af(x)dx+XAf(x)dx
=A1dxXA1dx

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