  Motivated by the works on Equivalence Principle in the context of linear
Generalized Uncertainty Principle and, independently, in the context of
quadratic Generalized Uncertainty Principle, we expand these endeavors in the
context of Generalized Uncertainty Principle when both linear and quadratic
terms in momentum are include. We demonstrate how the definitions of equations
of motion change upon that expansion. We also show how to obtain an analogue of
Liouville theorem in the presence of linear and quadratic Generalized
Uncertainty Principle. We employ the corresponding modified invariant unit
volume of phase space to discuss the resulting density of states, the problem
of cosmological constant, the black body radiation in curved spacetime, the
concurrent energy and consequent no Brick Wall entropy.
