Such a functional integral is extremely similar to the partition function in statistical mechanics. Indeed, it is sometimes called a partition function, and the two are essentially mathematically identical except for the factor of i in the exponent in Feynman's postulate 3. Analytically continuing the integral to an imaginary time variable (called a Wick rotation) makes the functional integral even more like a statistical partition function and also tames some of the mathematical difficulties of working with these integrals.