Publications

Books

Foundations of quantization for probability distributions. Lect. Notes in Math. 1730, Springer 2000 (jointly with H. Luschgy)

Contributions to Journals

Fractal functional quantization of mean-regular stochastic processes. Math. Proc. Camb. Phil. Soc. 150, 167-191 (2011) (jointly with H. Luschgy and G. Pagès)

Quantization for probability measures in the Prokhorov Metric. Theory Probab. Appl., Volume 53, No. 2, 216-241 (2009) (jointly with H. Luschgy)
Distortion mismatch in the quantization of probability measures. ESAIM: Probability and Statistics 12, 127-153 (2008) (jointly with H. Luschgy, G. Pagès)

Optimal quantizers for Radon random vectors in a Banach space. J. Approximation Theory 144, 27-53 (2007) (jointly with H. Luschgy, G. Pagès)
Quantization of probability distributions under norm-based distortion measures II: self-similar distributions. J. Math. Analysis Appl. 318, 507- 516 (2006) (jointly with S. Dellattre, H. Luschgy, G. Pagès)

Entropy-constrained functional quantization of Gaussian processes. Proc. Amer. Math. Soc. 133, 3403-3409 (2005) (jointly with H. Luschgy)

The point density measure in the quantization of self-similar probabilities. Math. Proc. Cambridge Phil. Soc 138, 513-531 (2005) (jointly with H. Luschgy)
Quantization of probability distributions under norm-based distortion measures. Statistics and Decisions 22, 261-282 (2004) (jointly with S. Dellattre, H. Luschgy, G. Pagès)
Sharp asymptotics of the metric entropy for ellipsoids. J. Complexity 20, 876-882 (2004) (jointly withH. Luschgy)
Quantization for probability measures with respect to the geometric mean error. Math. Proc. Camb. Phil. Soc. 136, 687-717 (2004) (jointly with H. Luschgy)
Functional quantization and small ball probabilities for Gaussian processes. J. Theor. Prob. 16, 1047-1062 (2003) (jointly with H. Luschgy und G. Pagès)
The quantization dimension of self-similar probabilities. Math. Nachrichten 241, 103-109 (2002) (jointly with H. Luschgy)
Rates of convergence for the empirical quantization error. Annals of Probability 30, 874-897 (2002) (jointly with H. Luschgy)
Asymptotics of the quantization errors for self-similar probabilities. Real Analysis Exchange 26, 795-810 (2000/01) (jointly with H. Luschgy)
The quantization of the Cantor distribution. Math. Nachr. 183, 113-133 (1997) (jointly with H. Luschgy)
On Bandt's tangential distribution for self-similar measures. Monatshefte für Mathematik 120, 223-246 (1995)
On the characterization of the Hausdorff measure on a self-similar set. Atti. Sem. Mat. Fis. Modena 42, 189-197 (1994)
Self-similar sets 7. A characterization of self-similar fractals with positive Hausdorff measure. Proc. Amer. math. Soc. 114, 995-1001 (1992) (jointly with C. Bandt)
The average error of quadrature formulas for functions of bounded variation. Rocky Mountain J. Math. 20, 707-716 (1990) (jointly with E. Novak)
A classification of disintegrations of measures. Contemporary Math. 94, 147-158 (1989) (jointly with R.D. Mauldin)
Bisection is not optimal on the average. Numer. Maths. 55, 481-491 (1989) (jointly with E. Novak)
The exact Hausdorff dimension in random recursive constructions. Mem. Amer. math. Soc. 71, No. 381 (1988) (jointly with R.D. Mauldin und S.C. Williams)
Statistically self-similar fractals. Probability Theory and Rel. Fields 74, 357-392 (1987)
Random homeomorphisms. Advances Math. 60, 239-359 (1986) (jointly with R.D. Mauldin und S.C. Williams)
Measurable one-to-one selections and transition kernels. Amer. J. Math. 106, 407-425 (1984) (jointly withR.D. Mauldin)
Isometries of measure algebras. Monatshefte für Mathematik 97, 107-118 (1984) (jointly with G. Mägerl)
Homomorphism compact spaces. Canadian J. Math. 35, 558-576 (1983) (jointly with A.G.A.G. Babiker)
Baire sections for group homeomorphisms. Proc. Amer. Math. Soc. 85, 615-618 (1982) (jointly with G. Mägerl)
Realizing automorphisms of quotients of product sigma-fields. Pacific J. Math. 99, 19-30 (1982)
A note on realizing homomorphisms of category algebras. General Topology and Its Appl. 12, 247-256 (1981)
A Radon-Nikodym theorem for capacites. J. reine u. angew. Math. 320, 192-214 (1980)
Induced sigma-homeomorphisms and a parametrization of measurable sections via extremal preimage measures. Math. Ann. 247, 67-80 (1980)
A measurable selection theorem for compact-valued maps. Manuscripta Math. 27, 341-352 (1979)
A selection theorem for Boolean correspondences. J. reine u. angew. Math. 295, 169-186 (1977)
On the existence of strong liftings in second countable topological spaces. Pacific J. Math. 58, 419-426 (1975)

Conference Proceedings

The quantization of probability distributions: Some results and open problems. Real Analysis Exchange Summer Symposium 2002, 87-102

Consistent estimation in the quantization problem for random vectors. In: Transaction of the 12th Prague Conference on Information Theory. Statistical Decision Functions, Random Processes, Acad. Sci. Czech Republic & Charles Univ. Prague, Prague 1994, pp. 84-87 (mit H. Luschgy)

Self-similar sets and measures. Rendiconti dell'istituto di matematica dell'universita di Trieste 26, 36-47 (1994)

Barnsley's scheme for the fractal encoding of images. J. Complexity 8, 72-78 (1992)

Note on question 4 of D. Maharam. In: Measure Theory, Oberwolfach 1983 (D. Kölzow, D. Maharam.Stone eds.), Lect. Notes in Math. 1089, Springer, Berlin-Heidelberg-New York 1984, p. 319

Random homeomorphisms (Kurzfassung). In: Measure Theory, Oberwolfach 1983 (D. Kölzow, D. Maharam.Stone eds.), Lect. Notes in Math. 1089, Springer, Berlin-Heidelberg-New York 1984, pp. 23-46 (mit R.D. Mauldin und S.C. Williams)

Selected results on measureable selections. In: Proc. of the Tenth Winter School on Abstract Analysis, Suppl. Rend. Circ. Mat. Palermo, Ser. II(2), 87-122 (1982)

Disintegration of a measure with respect to a correspondence. In: Measure Theory, Oberwolfach 1983 (D. Kölzow, D. Maharam.Stone eds.), Lect. Notes in math. 945, Springer, Berlin-Heidelberg-New York 1982, pp. 167-169 (with G. Mägerl)

Families of pairwise orthogonal measures. In: Proc. of the Ninth Winter School on Abstract Analysis, Czech. Acad. Sci., Prague 1981 (with G. Mägerl)

Measurable weak selections. In: Measure Theory, Oberwolfach 1979 (D. Kölzow ed.), Lect. Notes in Math. 794, Springer, Berlin-Heidelberg-New York 1980, pp. 117-140

On the existence of lower densities in noncomplete measure spaces. In: Measure Theory, Oberwolfach 1975 (D. Kölzow, A. Bellow eds.), Lect. Notes in Math. 541, Springer, Berlin-Heidelberg-New York 1976, pp. 155-158 (mit H. von Weizsäcker)

Reports

The quantization dimension of self-similar sets, MIP-9609, Universität Passau 1996

Foundations of quantization for random vectors. Preprint Nr. 16, Angewandte Mathematik und Informatik, Universität Münster 1994 (mit H. Luschgy)

The equidistribution on self-similar fractals. MIP-8929, Universität Passau 1989