Summary.
A classical theorem of S. Mazur and S. Ulam asserts that any surjective isometry between two normed spaces is an affine mapping. D. Mushtari proved in 1968 the same result in the case of random normed spaces in the sense of A. Sherstnev. The aim of the present paper is to show that the result holds also for the probabilistic normed spaces as defined by C. Alsina, B. Schweizer and A. Sklar, Aequationes Math. 46 (1993), 91–98.
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Supported by Grant CEEX-06-11-96.
Manuscript received: October 9, 2007 and, in final form, November 28, 2007.
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Cobzaş, S. A Mazur–Ulam theorem for probabilistic normed spaces. Aequ. math. 77, 197–205 (2009). https://doi.org/10.1007/s00010-008-2933-y
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DOI: https://doi.org/10.1007/s00010-008-2933-y