Deterministic Network Calculus

Appendix Mathematical Background

A.1. Non-decreasing functions

DEFINITION A.1 (Non-decreasing function).– A function is non-decreasing if

A.2. Infimum and supremum

DEFINITION A.2 (Infimum, Supremum).– Let . Then,

In particular, we have the following properties:

PROPOSITION A.1.– Let . Then:

1. 1)
2. 2)
3. 3)

PROPOSITION A.2 (Inf/Sup decomposition).– Let be two sets.

A.3. Continuity

DEFINITION A.3 (Left- and right-limits).– Let and . If they exist, then we denote the right-limit and