[20] N. Boboc, Gh. Bucur and A. Cornea: Carrier theory and negligible sets on a standard H-cone of functions. Rev. Roum. Pures Appl.

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5 INDEX absolutely continuous absorbent point adjoint autoadjoint reslovent autodual H-cone axiom D axiom of convergence axiom of nearly continuity axiom of polarity balayage balayage, representable base, essential base set basic set bounded kernel branching point carrier carrier map coercive cofine topology complement (of a balayage) complete maximum principle conatural topology continuous in order from below contraction convergence, axiom of dense in order from below Dirichlet space, functional, local syffiffietric dominant dominated domination principle ,

6 283 dual energy energy form essential base evaluation map excessive extreme ray fine sheaf property fine topology functional Dirichlet space generator Green function Green set harmonic carrier H-cone, autodual of functions, standard H-integral H-measure H-morphism Hunt's approximation theorem Hunt's theorem increasingly dense initial kernel Kakutani representation kernel bounded proper absolutely continuous local Dirichlet space lower semi-continuous regularization Lusin set Lusin space Markov canonical extension Markovian semigroup Mokobodzki neighbourhood Mokobodzki topology ,

7 284 natural extension natural sheaf property natural topology nearly continuity, axiom of nearly continuous nearly saturated negligible ordered convex cone P-excessive polar polarity, axiom of proper kernel pseudo-balayage Ray resolvent Ray semigroup reduite regular regularization, lower semi-continuous representable (balayage) resolvent, absolutely continuous associated with a semigroup autoadjoint Ray -s in duality strong Ray sub-markovian Riesz decomposition property saturated - I nearly semigroup Markovian Ray strong Ray sub-markovian semi-polar sheaf property, fine solid , 113, 141, , '3

8 285 ouslin set ouslin space specifically solid specific order standard Dirichlet space standard H-cone.. standard H-cone of functions tonian cone strictly positive strong Ray resolvent strong Ray semigroup sub-markovian resolvent sub-markovian semigroup substractible supermedian symmetric Dirichlet space T-balayage operator theorem of Doob-Bauer thin totally thin T-potential u- continuous unit, weak universally continuous everywhere V-dominant V-excessive V-negligible V-supermedian '1r-supermedian weak unit ,

9 INDEX OF YMBOL X A [f g] Ii.: sup F, inf F :N, lr, lr 'f V RVf V o, 'V R 1Y f 1)' -a.e. 'ttr A (,t) VF,!\F vt, At [] [J+ V F CJ f V [J g f+, f_, If I Rf..J..,"{,..A. ('f) Hom(,T) I Con() B f..., <p' ' B' R A s' b(a) b(b) ""* B A carr P(Y), H(Y) PA o(u), o K u Xu' u K l Xl' l l BA :ts (X) B(E) B+ 1 lim inf lr B d (B) B A B AA Bf P, H, P"', Hit- X p ' X;, X h' e, ell- E, E* *B A * If gx' gx' G,.u.' Gf' (G) H ' 'itt px P, P T p V p '1 Ker B u I l:> [It] , 10,