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Un esempio di trasformazione -Lipschitziana è dato da dove è compatta e è Lipschitziano. In questo articolo si mostra che se è una trasformazione -Lipschitziana regolare su uno spazio di Hilbert, allora vale anche il viceversa. Inoltre, ciò che è più importante, mostriamo che il coefficiente di Lipschitz per può essere scelto arbitrariamente prossimo all'-modulo di .
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