Possible Duplicate:
When $L_p = L_q$?
Can anyone tell me under what condition these two spaces $L^p(\mu)$ and $L^s(\mu)$ contain the same functions?
Asked
Active
Viewed 107 times
1
-
My bet (assuming $p\ne s$): Only when these spaces are finite dimensional, i.e., when the total space is the finite union of atoms. – Harald Hanche-Olsen Oct 25 '12 at 16:59
-
@HaraldHanche-Olsen: It seems that Nate's answer in When $L_p=L_q$? confirms your bet. – Oct 26 '12 at 17:32
-
@lp-man: Indeed it does. No surprise there. – Harald Hanche-Olsen Oct 26 '12 at 18:13