On the geometry of spheres in L-spaces |
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Authors: | J. J. Schäffer |
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Affiliation: | (1) Carnegie-Mellon University, Pittsburgh, Pennsylvania |
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Abstract: | It is shown that any two points on the surface of the unit ball ofL 1(μ), where the measureμ is non-atomic, may be joined in the surface by a curve whose length is equal to the straight-line distance between its endpoints. This property is contrasted with the metric properties of the unit sphere in other L-spaces. This work was supported in part by NSF grant GP-19126. |
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