Wednesday 25 April 2012

Functional Analysis MIT question/problem


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.




No comments:

Post a Comment