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Some results of probability measures on linear topological vector spaces with an application to Strassen’s log log law. (English) Zbl 0292.60007


MSC:

60B05 Probability measures on topological spaces
60J65 Brownian motion
28C20 Set functions and measures and integrals in infinite-dimensional spaces (Wiener measure, Gaussian measure, etc.)
Full Text: DOI

References:

[1] Badrikian, A., (Séminaire sur les Fonctions Aléatoires Linéaires et les Measures Cylindriques. Séminaire sur les Fonctions Aléatoires Linéaires et les Measures Cylindriques, Lecture Notes in Mathematics, Vol. 139 (1970), Springer-Verlag: Springer-Verlag New York) · Zbl 0209.48402
[2] Dudley, R.; Feldman, J.; LeCam, L., On seminorms and probabilities, and abstract Wiener spaces, Ann. of Math., Vol. 93, 390-408 (1971) · Zbl 0193.44603
[3] Gross, L., Lectures in Modern analysis and applications II, (Lecture Notes in Mathematics, Vol. 140 (1970), Springer-Verlag: Springer-Verlag New York) · Zbl 0194.30001
[4] Kanter, M., Linear sample spaces and stable processes, J. Functional Analysis, Vol. 9, 441-459 (1972) · Zbl 0232.60023
[5] Kelly, J. L.; Namioka, I., Linear Topological Vector Spaces (1963), D. Van Nostrand Co., Inc: D. Van Nostrand Co., Inc Princeton, NJ
[6] Kuelbs, J., Abstract Wiener spaces and applications to analysis, Pacific J. Math., 31, 433-450 (1969) · Zbl 0187.07001
[7] J. Kuelbs and R. LePageTrans. Amer. Math. Soc., to; J. Kuelbs and R. LePageTrans. Amer. Math. Soc., to · Zbl 0278.60052
[8] Kuelbs, J., Gaussian measures on a Banach space, J. Functional Analysis, 5, 354-367 (1970) · Zbl 0194.44703
[9] Segal, I. E., Distributions in Hilbert space and canonical systems of operators, Trans. Amer. Math. Soc., 88, 12-41 (1958) · Zbl 0099.12104
[10] Strassen, V., An invariance principle for the law of the interated logarithm, Z. Wahrscheinlickeitheorie, 3, 211-226 (1964) · Zbl 0132.12903
[11] Kuelbs, J., Expansions of vectors in a Banach space related to Gaussian measures, (Proc. Amer. Math. Soc., 27 (1971)), 364-370 · Zbl 0226.60060
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