indicator functions

• What Is the Derivative of an Indicator Function?
  An indicator function has classical derivative zero where it is locally constant and no derivative at jump points; distributionally, jumps become Dirac deltas.
• What Is the Derivative of an Indicator Function?
  An indicator function has ordinary derivative zero wherever it is locally constant; at jumps the derivative fails to exist, or is a delta distribution.
• What Is the Derivative of an Indicator Function, and Its Integral?
  An interval's indicator has ordinary derivative zero except at its jumps; its integral is overlap length, and its distributional derivative records those jumps.