Question

Jump of a function is defined as​

Answer 1

Answer:

The function fj is the jump part of f (or jump function of f, using the terminology of Lebesgue [Le]) and it is defined by fj(x)=∑y≤xf(y+)−f(y−).

Answer 2

Answer:

A function has a jump discontinuity at = if both one-sided limits as approaches exist but are unequal. Those limits can exist without the function being defined at = . Thus, the function doesn't have to be defined at = to have a jump discontinuity there.