The symmetric derivative

Larson, Lee

doi:10.1090/S0002-9947-1983-0694378-6

The symmetric derivative
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Trans. Amer. Math. Soc. 277 (1983), 589-599 Request permission

Abstract:

It is shown that all symmetric derivatives belong to Baire class one, and a condition characterizing all measurable symmetrically differentiable functions is presented. A method to find a well-behaved primitive for any finite symmetric derivative is introduced, and several of the standard theorems of differential calculus are extended to include the symmetric derivative.

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