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References
P. Billingsley, Convergence of types in k-spaces, Z.Wahrscheinlichkeitstheorie verw. Geb. 5(1966), pp.175–179.
B.V.Gnedenko and A.N.Kolmogorov, Limit distributions for sums of independent random variables, Moscow 1949 (in Russian).
M.G. Hahn, The generalized domain of attraction of a Gaussian law on Hilbert spaces, Lecture Notes in Math. 709 (1979), pp.125–144.
M.G.Hahn and M.J.Klass, Matrix normalization of sums of i.i.d. random vectors in the domain of attraction of the multivariate normal, Ann. of Probability (in print).
N.C. Jain, Central limit theorem in a Banach space, Lecture Notes in Math. 526 (1975), pp.113–130.
R. Jajte, Semi-stable probability measures on R N, Studia Math. 61 (1977), pp.29–39.
O. Jouandet, Sur la convergence en type de variables aléatoires á valuers dans des espaces d’Hilbert on de Banach, C.R. Acad. Sc. Paris 271 (1970), série A, pp.1082–1085.
Z.J.Jurek, Remarks on operator-stable probability measures, Coment. Math. XXI (1978).
Z.J.Jurek, Central limit theorem in Euclidean spaces, Bull. Acad. Pol. Sci. (in print).
Z.J.Jurek, Domains of normal attraction of operator-stable measures on Euclidean spaces, ibidem (in print).
Z.J.Jurek, Gaussian measure as an operator-stable and operator-semistable distribution on Euclidean space, Probability and Mathematical Statistics, (in print).
Z.J.Jurek, On Gaussian measure on R d, Procedings of 6th Conference on Probability Theory, Brasov 1979 (in print).
Z.J.Jurek, Domains of normal attraction for G-stable measures on R d, Teor. Verojatnost. i Primenen. (in print).
Z.J.Jurek and J.Smalara, On integrability with respect to infinitely divisible measures, Bull. Acad. Pol. Sci. (in print).
W.Krakowiak, Operator-stable probability measures on Banach spaces, Colloq. Math. (in print).
J. Kucharczak, On operator-stable probability measures, Bull. Acad.Pol.Sci. 23 (1975), pp.571–576.
J. Kucharczak, Remarks on operator-stable measures, Colloq. Math. 34 (1976), pp.109–119.
J. Kucharczak and K. Urbanik, Operator-stable probability measures on some Banach spaces, Bull. Acad. Pol. Sci. 25 (1977), pp.585–588.
A. Kumar, Semi-stable probability measures on Hilbert spaces, J. Multivar. Anal. 6 (1976), pp.309–318.
A.Łuczak, Operator-semistable probability measures on R N, Thesis, Łódź University (preprint in Polish).
B.Mincer, Complety stable measures on R n, Comentationes Math. (in print).
B.Mincer and K.Urbanik, Completely stable measures on Hilbert spaces, Colloq. Math. (in print).
K.R. Parthasarathy, Every completely stable distribution is normal, Sankhya 35 (1973), Serie A, pp.35–38.
K.R. Parthasarathy and K. Schmidt, Stable positive definite functions, Trans. Amer. Math. Soc. 203 (1975), pp. 161–174.
Ju.V. Prohorov, Convergence of random processes and limit theorems in probability theory, Teor. Verojatnost. i Primenen. 1 (1956), pp.173–238 (in Russian).
K. Schmidt, Stable probability measures on R v, Z. Wahrscheinlichkeitstheorie verw. Gebiete 33 (1975), pp.19–31.
S.V. Semovskii, Central limit theorem, Doklady Akad.Nauk SSSR 245(4), 1979, pp.795–798.
M. Sharpe, Operator-stable probability measures on vector groups, Trans. Amer. Math. Soc. 136 (1969), pp.51–65.
K. Urbanik, Lévy’s probability measures on Euclidean spaces, Studia Math. 44 (1972), pp.119–148.
K. Urbanik, Decomposability properties of probability measures, Sankhya 37 (1975), Serie A, 530–537.
K. Urbanik, Lévy’s probability measures on Banach spaces, Studia Math. 63 (1978), pp.283–308.
I. Weismann, On convergence of types and processes in Euclidean spaces, Z. Wahrscheinlichkeitstheorie verw. Gebiete 37 (1976), pp.35–41.
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Jurek, Z.J. (1980). On stability of probability measures in euclidean spaces. In: Weron, A. (eds) Probability Theory on Vector Spaces II. Lecture Notes in Mathematics, vol 828. Springer, Berlin, Heidelberg. https://doi.org/10.1007/BFb0097399
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