Abstract
We study the problem to what extent a measure is determined by its values on a family of balls and how it might possibly be computed from those values.
Keywords
- Convex Cone
- Gaussian Measure
- Small Ball
- Positive Borel Measure
- General Banach Space
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References
A. S. Besicovitch, A general form of the covering principle and relative differentiation of additive functions, Proc. Camb. Phil. Soc. 41 (1945), 103–110.
C. Borell, A note on Gaussian measures which agree on small balls, Ann. Inst. Henri. Poincare 13, (1977), 231–238.
Jens Peter Reus Christensen, On some measures analogous to Haar measure, Math. Scand. 26 (1970), 103–106.
Jens Peter Reus Christensen, Uniform measures and spherical harmonics, Math. Scand. 26 (1970), 293–302.
Jens Peter Reus Christensen, The small ball theorem for Hilbert spaces, Math. Ann. 237 (1978), 273–276.
Jens Peter Reus Christensen and Wojchiech Herer, On the existence of pathological submeasures and the construction of exotic topological groups, Math. Ann. 213 (1975), 203–210.
R. O. Davis, Measures not approximable or specificable by means of balls, Mathematica 18 (1971), 157–160.
J. Hoffmann-Jørgensen, Measures which agree on balls, Math. Scand. 37 (1975), 319–326.
D. Preiss, Gaussian measures and covering theorems, Commentationes Matematicae Universitatis Carolinae 20, 1 (1979).
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© 1980 Springer-Verlag
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Christensen, J.P.R. (1980). A survey of small ball theorems and problems. In: Kölzow, D. (eds) Measure Theory Oberwolfach 1979. Lecture Notes in Mathematics, vol 794. Springer, Berlin, Heidelberg. https://doi.org/10.1007/BFb0088208
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DOI: https://doi.org/10.1007/BFb0088208
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Publisher Name: Springer, Berlin, Heidelberg
Print ISBN: 978-3-540-09979-6
Online ISBN: 978-3-540-39221-7
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