Download Complex Analysis — Fifth Romanian-Finnish Seminar: Part 1 by Olli Lehto (auth.), Cabiria Andreian Cazacu, Nicu Boboc, PDF

By Olli Lehto (auth.), Cabiria Andreian Cazacu, Nicu Boboc, Martin Jurchescu, Ion Suciu (eds.)

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E. We observe first that the differentiability abstract Wiener space to th9 analytic defini- in D. Thus,we are in the hypothe- 40 ses of the preceding proposition,so ~hat we are allowed to conclude that ~i~ exceptional se~ EocD,where f is not Aro-szajn difzerentiable, is in ~ and then,on account of proposition 3,Eo is a Gaussian null set, implying piEo:O,as desired. e. sense in D,~he scalar deriva- in D. 10),we obtain Lemma 5 . ~ > 0 and for every Borel set Ec(i,H,B)(separable),there is:a compact set K c E such that pI(E-K )<¢.

T B is the ~-algebra of Bore l sets of B. 2 o ~ ( a = }={ E 6A~; EJjE=, E=6 ~ ( a m )), where (a m }CB with a=#~D (m~N). %~m~B=~~a=},where (a m } complete the inteT'section is taken over all sequences in B. iowever,we established ([7],lemaa 3) that each class of ezceptional sets from above co in cides with the cotresponding class defined by Aronszajn. measure . e. e. when B=H),we obtain the usual definitima m~ntioned at the begizming of this paper and where f corresponds to the l-dimensional pro je ction.

G. Sarvas,la me- sure Lebesgue de Bf et de f (Bf) est nulle et l~ur dimension de Hausdorf~~est _< n. Comm~ dernler exemple d'extension du Th6or~me 3 de Stoilow,mentionnons les importantes contributions appo~t4es par O ° ~ r t l o et U. Srebro dans le m4molre "On the local behavior of quasi-regular maps and branched covering maps" (J°d'Analyse Math° ,36 (1979) ,198-212). Martlo et Srebro appellent application de recouvrement ramifi~ route transformation contlnu~,ouvert~ et discr~te. Martio formes du Th~or~me Si f : S - ~ S est une application et 3 d6 Stoilow pour n=2: de recouvrcmcnt ramifi~,alors il existe I.

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