prove (without using thm 4.4.10 ): if each F_n is integrable and {F_n} converges uniformly on [a, b],then  exists.

thm 4.4.10 Suppose that {F_n}converges pointwise to F and each F_n is integrable on[a, b].

a) if the converges is uniform, then Fis integrabel on [a, b] and  holds.

b) If the sequence {||F_n||[a,b]} is bounded and F is integrable on [a, b], then holds.  
 

Transcribed Image Text:

lim, ff, dx lim, ff, dx

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aGiven that if each fn is integrable andfn converges uniformly on ab let 0 be any number ... View the full answer