Complex sentence: To do this, one first finds a condition that is weaker than absolute continuity but is satisfied of any differentiable function: this is the concept of "generalized" absolute continuity; generalized absolutely continuous functions will be exactly those functions which are indefinite Khinchin integrals.
Split into simpler sentences: To do this, one first finds a condition that is weaker than absolute continuity but is satisfied by any differentiable function. This is the concept of "generalized" absolute continuity; generalized absolutely continuous functions will be exactly those functions which are indefinite Khinchin integrals.