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azz ze Oz ax' dy dxdy 10. Suppose that a monotone sequence of continuous functions { fn} converges pointwise to a continuous function F on some...

7710000this is a real analysis problem that I need help with

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azz
ze
Oz
ax'
dy
dxdy
10. Suppose that a monotone sequence of continuous functions { fn}
converges pointwise to a continuous function F on some closed interval
[a, b]. Prove that the convergence is uniform.
Note: In this problem by a monotone sequence of functions we mean a
sequence fn such that either fn (x ) < fn+1 (x) for all n and all x E [a, b],
or fn (x ) 2 fn+1 (x) for all n and all x E [a, b].
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