Q: Consider a real-valued function f : R −→ R which is locally integrable in the

sense that

(5.2) gL(x) =

f(x) x ∈ [−L,L]

0 x ∈ R \ [−L,L]

is Lebesgue integrable of each L ∈ N.

A:

f: R ---> R

locally integrable

(5.2) Greenland[gL](x) =

function (x) x is an element of [-L,L]

0 x is an element of R divided by [-L,L]

Lebesgue integrable = L is an element of N

5.2gL f (R) =

L = R + L + (- L)

A little confused on this.

Hope you can correct and leave a comment.

Thanks.