Sur la discontinuité approximative et la dérivée approximative

Infinite approximate Peano derivatives

“…In case (n + 1) is odd, for sufficiently small h we can select h 1 ∈ V x such that h < h 1 < h 2 . The monotonicity of f yields the same inequality as in (9). Taking the limit we get the desired result.…”

“…The case n = 0 requires special attention. From this definition, it follows that [9], [10], and [11]. )…”

A Modest Review of a Great Deal of Work

“…Z. Zahorski, in [63] asked what could be said if "derivative" was replaced by "approximate derivative" and "continuity" by "approximate continuity." In 1963 Jan answers this in his paper [27]. Theorem 1.16.…”

“…In 1963, [27] Jan answered yet another question of Zahorski, this time asked in 1948, in [63]. Here he first proves the following theorem.…”