HISTORICAL ESSAY ON CONTINUITY OF DERIVATIVES - sci.math | Google Groups: "a derivative is a Baire one function, which implies that any

derivative is continuous on the complement of a first category set.

Moreover, since the set of points at which an arbitrary function

is not continuous is an F_sigma set, it follows that the

non-continuity points of any derivative must be an F_sigma

first category set. In addition, because every derivative

satisfies the intermediate value property, no derivative can

have a jump discontinuity. (This was also pointed out by Kovarik.)"

Could. Not. Decipher.

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