Before revision:  At last, based on the Ekeland's variational principle for a proper lower semicontinuous- \bar{L} ^{0 function, we show that \epsilon-subdifferentials can be approximated by subdifferentials.
After revision:  At last, based on the Ekeland's variational principle for a proper lower semicontinuous- \bar{L} ^0--valued function, we show that \epsilon-subdifferentials can be approximated by subdifferentials.