Question: 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

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

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

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

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

lim, ff, dx

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