By Lars V. Ahlfors (auth.), Julian Ławrynowicz (eds.)
Read or Download Analytic Functions Kozubnik 1979: Proceedings of a Conference Held in Kozubnik, Poland, April 19–25, 1979 PDF
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Additional resources for Analytic Functions Kozubnik 1979: Proceedings of a Conference Held in Kozubnik, Poland, April 19–25, 1979
Sample text
Again the proof is identical with the proof of the theorem that is a Banach algebra. S 36 Some 4. THE SPACE Notation. ,tn) l a < t l < t Definition. Let Borel measures on tion of ~ Algebras over ~ × ~n An× ~n ~ 8n Let n v) m ~#~(An X ing class of meas~tres on Definition. 1 ~ var ~ ~ the total varia- ~n((a,b]n×R n~) be ~ let tom a. ,t n) EAn, the correspond- (a,b] n X ~ n v . , n where the infimum is taken over all ~'s so that F and ~ are related by (~ . 2 ) . 0. For each Proof. Let FE Sn" n = i~2, ...
18) is an element of F£S'n ^ Next, in order to show that subsets of J H£Sn-1 , we define triangular arrays of by a two dimensionaD_ inductive process. Thus Let "~l,e --- {(~x~)l(Tx~/e J , tl= t 2] ; ~1,2 =- ~- ~1,2 ' ~l, 3 - - [ ( ~ X ~ ) I ( ~ X ~ ) 6 ~ l , . ° 2 , tl=t3] ~ ~1,3-=~1,2-~1,3 . j must be disjoint, j
j ~n-l~n ; ~n_l,n=~n_2,n-~n_l,n and all k>j and also t = t ~ and for each P q and also for is empty, and this is impossible j= p and since in this set since ~n-l, n C ~ .
2 , tl=t3] ~ ~1,3-=~1,2-~1,3 . j must be disjoint, j
j ~n-l~n ; ~n_l,n=~n_2,n-~n_l,n and all k>j and also t = t ~ and for each P q and also for is empty, and this is impossible j= p and since in this set since ~n-l, n C ~ . 23) is an element ^ of ^ Sn_ I , and will thus prove that Definition. 24) V' k,p-1 ti=tl, t2=t2, = V' k,l = V k,p-1 Vk~l ~ ~ H6 Sn_ I V' , E a Borel set, let )I (~,v) 6Jp, q , (t',v')E E where "" . t'q - l = t q - 1 "'" t'n-1 = t n k~2--- Vk, 2 ~ -vt~,p-Vk, p+Vk,q' V'k~q-Vk, q+l ~ " ..
