For n yen 1, let f n be real valued measurable functions defined on an open set E R containing 0, and suppose that f n ( x ) pound M ( yen ) for all n and all x Atilde E , and that For x Atilde E Then show that, for any sequence There exists a subsequence x m Atilde x n and a l null subset N of E (...

The limits are taken as n or subsequences thereof tend to Let be the df of the N ...

For n ¥ 1, let f n be real-valued measurable functions defined on an open set E

Question:

Forn‰¥ 1, letf_nbe real-valued measurable functions defined on an open setEŠ‚ R containing 0, and suppose that |f_n(x)| £M(< ¥) for allnand allxÃŽE, and that

For x ÃŽ E. Then show that, for any sequence

There exists a subsequence {x_m} Ã {x_n} and a l=null subset N of E (which may depend on {x_n}) such that f_m(x+ x_m) here l is the Lebesgue measure?