An involution of reals, discontinuous on rationals, and whose derivative vanishes a.e.

An involution of reals, discontinuous on rationals, and whose derivative vanishes a.e.

We study the involution of the real line, induced by Dyer’s outer automorphism of PGL(2,Z). It is continuousat irrationals with jump discontinuities at rationals. We prove that its derivative exists almost everywhere and vanishesalmost everywhere.

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