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On Universal Primitive Functions
Xiao-Xiong Gan and Karl R. Stromberg
Proceedings of the American Mathematical Society
Vol. 121, No. 1 (May, 1994), pp. 151-161
Published by: American Mathematical Society
Stable URL: http://www.jstor.org/stable/2160376
Page Count: 11
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This paper generalizes Marcinkiewicz's universal primitive on pointwise a.e. convergence directly to higher-dimensional spaces. It is also proved that the set of all universal primitive functions with respect to some given nonzero null sequence is residual and, hence, dense in the Banach space C(In, Rm) ∀ n, m ∈ N.
Proceedings of the American Mathematical Society © 1994 American Mathematical Society