Càdlàg Functions

Càdlàg functions are a class of functions characterized by having paths that are right-continuous with left limits. This means that at any given point, the function's value approaches from the left (the limit from smaller inputs) and the value itself is equal to the limit from the right (the limit from larger inputs). These functions can have jumps or sudden changes, but no "discontinuity gaps" from the right; they are predictable and well-behaved in terms of limits. Càdlàg functions are important in fields like probability and stochastic processes because they model phenomena that evolve continuously with occasional sudden shifts.