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On the nonexistence of unimodular functions in $ R\sp{2}(X,\,dx\,dy)$

Author: Alfred G. Brandstein
Journal: Proc. Amer. Math. Soc. 49 (1975), 339-341
MSC: Primary 46E15; Secondary 30A98
MathSciNet review: 0367632
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Abstract: It is shown for certain planar sets, e.g., Brennan sets, with no interior, that if $ f \in {R^2}(X,dxdy)$ and $ \vert f\vert = 1\;$   a.e.$ \; dxdy$ then $ f \equiv$   constant .

References [Enhancements On Off] (What's this?)

  • [1] A. G. Brandstein, Function spaces related to hypo-Dirichlet algebras, Doctoral Dissertation, Brown University, Providence, R. I., 1972.
  • [2] James E. Brennan, Invariant subspaces and rational approximation, J. Functional Analysis 7 (1971), 285–310. MR 0423059
  • [3] -, Approximation in the mean and quasi-analyticity, University of Kentucky, Math. Dept., 1972.
  • [4] Kenneth Hoffman and Hugo Rossi, Extensions of positive weak*-continous functionals, Duke Math. J. 34 (1967), 453–466. MR 0225168

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Keywords: Bounded point evaluation, Brennan set
Article copyright: © Copyright 1975 American Mathematical Society

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