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Because of unboundedness of the general relativity action, Euclidean versionof the path integral in general relativity requires definition. Area tensorRegge calculus is considered in the representation with independent area tensorand finite rotation matrices. Being integrated over rotation matrices the pathintegral measure in area tensor Regge calculus is rewritten by movingintegration contours to complex plain so that it looks as that one witheffective action in the exponential with positive real part. We speculate thatpositivity of the measure can be expected in the most part of range ofvariation of area tensors.

On positivity of quantum measure and of effective action in area tensor Regge calculus