Continuous transformation of Baire measures into Lebesgue measure

Kellerer, Hans

doi:10.1090/S0002-9939-02-06505-X

Continuous transformation of Baire measures into Lebesgue measure
HTML articles powered by AMS MathViewer

by Hans G. Kellerer PDF

Proc. Amer. Math. Soc. 130 (2002), 2305-2309 Request permission

Abstract:

A recent result by Wulbert on the existence of continuous functions with measure zero level sets is slightly extended and its proof is considerably simplified. As a by–product, a criterion is established for a Baire measure to allow a continuous transformation into Lebesgue measure.

References

Charles R. Hobby and John R. Rice, A moment problem in $L_{1}$ approximation, Proc. Amer. Math. Soc. 16 (1965), 665–670. MR 178292, DOI 10.1090/S0002-9939-1965-0178292-5
Hans G. Kellerer, Zur Existenz analoger Bereiche, Z. Wahrscheinlichkeitstheorie und Verw. Gebiete 1 (1962/63), 240–246 (German). MR 156940, DOI 10.1007/BF00532495
Hans G. Kellerer, A topological version of Liapunov’s theorem, Arch. Math. (Basel) 72 (1999), no. 3, 206–213. MR 1671279, DOI 10.1007/s000130050323
R. R. Phelps, Uniqueness of Hahn-Banach extensions and unique best approximation, Trans. Amer. Math. Soc. 95 (1960), 238–255. MR 113125, DOI 10.1090/S0002-9947-1960-0113125-4
Daniel Wulbert, Liapanov’s and related theorems, Proc. Amer. Math. Soc. 108 (1990), no. 4, 955–960. MR 1005716, DOI 10.1090/S0002-9939-1990-1005716-8
Patrick N. Dowling, Isometric copies of $c_0$ and $l^\infty$ in duals of Banach spaces, J. Math. Anal. Appl. 244 (2000), no. 1, 223–227. MR 1746799, DOI 10.1006/jmaa.2000.6714