Summary.
Motivated by previous papers dealing with mappings preserving the inner product almost everywhere as well as by stability results for the orthogonality equation we investigate a combination of these two problems. We show that a mapping that preserves inner product approximately and up to a negligible set of arguments has to be almost everywhere close to an exact solution of the orthogonality equation.
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Received: October 9, 1998; revised version: June 22, 1999.
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Chmieliński, J. Almost approximately inner product preserving mappings. Aequ. math. 59, 214–221 (2000). https://doi.org/10.1007/s000100050121
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DOI: https://doi.org/10.1007/s000100050121