Natural extension of the Generalised Uncertainty Principle

We discuss a gedanken experiment for the simultaneous measurement of the position and momentum of a particle in de Sitter spacetime. We propose an extension of the so-called generalized uncertainty principle (GUP) which implies the existence of a minimum observable momentum. The new GUP is directly connected to the nonzero cosmological constant, which becomes a necessary ingredient for a more complete picture of the quantum spacetime.