[分析] 想問一個複變證明

[Bourbaki (大狐狸)]

Suppose {F_i} is a sequence of holomorphic function on the open set Ω.
If there exist constants c_i > 0 such that
Σc_i<∞ and |F_i(z)-1| < c_i for all z in Ω.

                      n                               ∞
Want To Show f_n(z)= Π F_i(z) converges uniformly to Π F_i(z)
                      1                                1
請問要怎麼做uniformly的部份呢

謝謝^^

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推 Xixan       :我個人覺得還滿難只證converge不證到uniformly的
→ Xixan       :何必再仔細看看，如果還不行就PO一下做法吧@@
→ Bourbaki    :不會  竹點收斂還滿好正的
→ Xixan       :我的意思是，逐點收斂通常會被uniform一起證完…
→ Xixan       :                          把