Ritter, G. On Kakutani’s dichotomy theorem for infinite products of not necessarily independent functions. (English) Zbl 0377.28004 Math. Ann. 239, 35-53 (1979). Page: −5 −4 −3 −2 −1 ±0 +1 +2 +3 +4 +5 Show Scanned Page Cited in 1 ReviewCited in 4 Documents MSC: 28A35 Measures and integrals in product spaces 60B05 Probability measures on topological spaces 60F20 Zero-one laws PDF BibTeX XML Cite \textit{G. Ritter}, Math. Ann. 239, 35--53 (1979; Zbl 0377.28004) Full Text: DOI EuDML References: [1] Bauer, H.: Über die Beziehungen einer abstrakten Theorie des Riemann-Integrals zur Theorie Radonscher Maße. Math. Z.65, 448-482 (1956) · Zbl 0073.04003 [2] Brown, G.: Riesz products and generalized characters. Proc. Lond. Math. Soc.30, 209-238 (1975) · Zbl 0325.43003 [3] Brown, G., Moran, W.: A dichotomy for infinite convolutions of discrete measures. Proc. Camb. Phil. Soc.73, 307-316 (1973) · Zbl 0247.43002 [4] Brown, G., Moran, W.: On orthogonality of Riesz products. Proc. Camb. Phil. Soc.76, 173-181 (1974) · Zbl 0282.43001 [5] Edwards, R.E.: Functional analysis. New York-Chicago-San Francisco-Toronto-London: Holt, Rinehart and Winston 1965 · Zbl 0182.16101 [6] Hewitt, E., Ross, K.A.: Abstract Harmonic Analysis II. Berlin-Heidelberg-New York: Springer 1970 · Zbl 0213.40103 [7] Hewitt, E., Zuckerman, H.S.: Singular measures with absolutely continuous convolution squares. Proc. Camb. Phil. Soc.62, 399-420 (1966), Corrigendum, ibid.63, 367-368 (1967) · Zbl 0148.38101 [8] Jacobs, K.: On Poincaré’s recurrence theorem. Proceedings of the Fifth Berkeley Symposium on Mathematical Statistics and Probability 375-404 (1965/66) [9] Jessen, B., Wintner, A.: Distribution functions and the Riemann zeta function. Trans. Amer. Math. Soc.38, 48-88 (1935) · JFM 61.0462.03 [10] Kakutani, S.: On equivalence of infinite product measures. Ann. of Math.49, 214-224 (1948) · Zbl 0030.02303 [11] Kanter, M.: Equivalence singularity dichotomies for a class of ergodic measures. Math. Proc. Camb. Phil. Soc.81, 249-252 (1977) · Zbl 0383.60041 [12] Peyrière, J.: Sur les produits de Riesz. C.R. Acad. Sc. Paris276, 1417-1419 (1973) · Zbl 0258.43002 [13] Peyrière, J.: Etude de quelques propriétés des produits de Riesz. Ann. Inst. Fourier25, 127-169 (1975) · Zbl 0302.43003 [14] Ritter, G.: Unendliche Produkte unkorrelierter Funktionen auf kompakten, abelschen Gruppen. Math. Scand.42 (1978) · Zbl 0398.42013 [15] Ritter, G.: On dichotomy of Riesz products and generalized Riesz products. To appear in Math. Proc. Camb. Phil. Soc. · Zbl 0405.43007 [16] Skorokhod, A.V.: Integration in Hilbert space. Berlin-Heidelberg-New York: Springer 1974 · Zbl 0307.28010 [17] Stout, W.F.: Almost sure convergence. New York-San Francisco-London: Academic Press 1974 · Zbl 0321.60022 [18] Tjur, T.: Conditional Probability Distributions. University of Copenhagen: Institute of Mathematical Statistics 1974 [19] Wintner, A.: The Fourier transforms of probability distributions. Baltimore: The John Hopkins University 1947 · Zbl 0034.04001 This reference list is based on information provided by the publisher or from digital mathematics libraries. Its items are heuristically matched to zbMATH identifiers and may contain data conversion errors. It attempts to reflect the references listed in the original paper as accurately as possible without claiming the completeness or perfect precision of the matching.