Measurability. Gravity and gauge theories in measurable form at low and high energies

In this paper the author formulates a gauge field theory in terms of the measurability notion introduced in his previous works and performs a comparative analysis of passage to high energies for gravity and gauge theories. It has been found that measurability in gravity is in close association with quantum fluctuations of the space-time geometry (or at high energies with the ”space-time foam”) introduced by J.A.Wheeler. It is demonstrated that at low energies E Ep, in terms of measurable quantities, we can correctly define the Least Action Principle and Noether’s Theorem.