Metric properties of generalized Cantor products

 Access to full text

 Full (PDF)

1. [Eng] F. Engel, Entwicklung der Zahlen nach Stammbrüchen, in: Verhandlungen des 52sten Versammlung deutscher Philologen und Schulmänner in Marburg vom 29. September bis 3. October 1913, Leipzig 1914, 190-191. 
2. [Esc] E. B. Escott, Rapid method for extracting a square root, Amer. Math. Monthly 44 (1937), 644-646. Zbl63.0525.05
3. [Ga-Ko] I. S. Gál et J. F. Koksma, Sur l'ordre de grandeur des fonctions sommables, C. R. Acad. Sci. Paris 227 (1948), 1321-1325. Zbl0041.02404
4. [Gal] J. Galambos, Representations of Real Numbers by Infinite Series, Lecture Notes in Math. 502, Springer, 1976. Zbl0322.10002
5. [Go-Sm] C. Goldie and R. L. Smith, On the denominators in Sylvester's series, Proc. London Math. Soc. (3) 54 (1987), 445-476. Zbl0587.10028
6. [Khi] A. Ya. Khinchin, Continued Fractions, 3rd ed., Phoenix Books, The University of Chicago Press, 1935. 
7. [Kn-Kn] A. Knopfmacher and J. Knopfmacher, A new infinite product representation for real numbers, Monatsh. Math. 104 (1987), 29-44. Zbl0624.10008
8. [Ku-Ni] L. Kuipers and H. Niederreiter, Uniform Distribution of Sequences, Pure and Appl. Math., Wiley Interscience Series of Texts, Monographs, and Tracts, 1974. 
9. [La-Th] Y. Lacroix and A. Thomas, Number systems and repartition mod 1, J. Number Theory, to appear. 
10. [MF-VP] M. Mendès France and A. J. van der Poorten, From geometry to Euler identities, Theoret. Comput. Sci. 65 (1989), 213-220. 
11. [Opp] A. Oppenheim, On the representation of real numbers by products of rational numbers, Quart. J. Math. Oxford Ser. (2) 4 (1953), 303-307. Zbl0053.03903
12. [Ost] A. Ostrowski, Über einige Verallgemeinerungen des Eulerschen Produktes ${\prod }_{\nu =0}^{\infty }(1+x^{2^{\nu }})=1/(1-x)$, Verh. Naturforsch. Ges. Basel 11 (1929), 153-214. 
13. [Per] O. Perron, Irrazionalzahlen, Chelsea, New York 1948. 
14. [Pet] K. Petersen, Ergodic Theory, Cambridge Stud. Adv. Math. 2, Cambridge University Press, 1983. 
15. [Phi] W. Philipp, Some metrical theorems in number theory, Pacific J. Math. 20 (1967), 109-127. Zbl0144.04201
16. [Sch] F. Schweiger, Ergodic properties of fibered systems, draft version, Institut für Math. der Universität Salzburg, 1989. 
17. [Sch-1] F. Schweiger, Metrische Sätze über Oppenheimentwicklungen, J. Reine Angew. Math. 254 (1972), 152-159. Zbl0234.10040
18. [Sie-1] W. Sierpiński, On certain expansions of real numbers into infinite fast converging products, Prace Mat. 2 (1958), 131-138 (in Polish; Russian and English summaries). 
19. [Sie-2] W. Sierpiński, Généralisation d'une formule de E. B. Escott pour les racines carrées, Bull. Soc. Roy. Sci. Liège 22 (1953), 520-529. Zbl0053.03904
20. [Sta] P. Stambul, private communication. 
21. [Ver] W. Vervaat, Success Epochs in Bernoulli Trials (with Applications in Number Theory), Math. Center Tracts 42, Mathematisch Centrum, Amsterdam 1972. 

1. A. Iwanik, Y. Lacroix, Some constructions of strictly ergodic non-regular Toeplitz flows