Closed sets without measurable matching

Laczkovich, M.

doi:10.1090/S0002-9939-1988-0947676-2

Closed sets without measurable matching
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by M. Laczkovich

Proc. Amer. Math. Soc. 103 (1988), 894-896

DOI: https://doi.org/10.1090/S0002-9939-1988-0947676-2

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Abstract:

We construct a rectangle in the unit square such that its perimeter contains a matching (i.e. the graph of a bijection of the unit interval onto itself) but does not contain a Borel matching or a matching measurable with respect to the linear measure.

References

Béla Bollobás, Graph theory, Graduate Texts in Mathematics, vol. 63, Springer-Verlag, New York-Berlin, 1979. An introductory course. MR 536131
Siegfried Graf and R. Daniel Mauldin, Measurable one-to-one selections and transition kernels, Amer. J. Math. 107 (1985), no. 2, 407–425. MR 784290, DOI 10.2307/2374421
Paul R. Halmos, Lectures on ergodic theory, Publications of the Mathematical Society of Japan, vol. 3, Mathematical Society of Japan, Tokyo, 1956. MR 0097489
J. Kaniewski and C. A. Rogers, Double uniformization, J. London Math. Soc. (2) 22 (1980), no. 3, 521–533. MR 596330, DOI 10.1112/jlms/s2-22.3.521

Sur les correspondences multivoques des ensembles

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R. Daniel Mauldin, One-to-one selections—marriage theorems, Amer. J. Math. 104 (1982), no. 4, 823–828. MR 667537, DOI 10.2307/2374207
R. Rado, Factorization of even graphs, Quart. J. Math. Oxford Ser. 20 (1949), 95–104. MR 30202, DOI 10.1093/qmath/os-20.1.95
V. N. Sudakov, The independent complement to two decompositions in the case of the existence of bounded density, Trudy Mat. Inst. Steklov. 111 (1970), 3–11. (errata insert) (Russian). MR 0290423