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An important aspect in defining a path integral quantum theory is thedetermination of the correct measure. For interacting theories and theorieswith constraints, this is non-trivial, and is normally not the heuristic"Lebesgue measure" usually used. There have been many determinations of ameasure for gravity in the literature, but none for the Palatini or Holstformulations of gravity. Furthermore, the relations between different resultingmeasures for different formulations of gravity are usually not discussed.  In this paper we use the reduced phase technique in order to derive thepath-integral measure for the Palatini and Holst formulation of gravity, whichis different from the Lebesgue measure up to local measure factors which dependon the spacetime volume element and spatial volume element.  From this path integral for the Holst formulation of GR we can also give anew derivation of the Plebanski path integral and discover a discrepancy withthe result due to Buffenoir, Henneaux, Noui and Roche (BHNR) whose origin weresolve. This paper is the first in a series that aims at better understandingthe relation between canonical LQG and the spin foam approach.

Canonical path integral measures for Holst and Plebanski gravity. I. Reduced Phase Space Derivation