Editing Path integral formulation (section)

=== Measure-theoretic factors ===
Sometimes (e.g. a particle moving in curved space) we also have measure-theoretic factors in the functional integral:
: <math>\int \mu[x] e^{iS[x]} \,\mathcal{D}x.</math>
This factor is needed to restore unitarity.

For instance, if
: <math>S = \int \left( \frac{m}{2} g_{ij} \dot{x}^i \dot{x}^j - V(x) \right) \,dt,</math>
then it means that each spatial slice is multiplied by the measure {{math|{{sqrt|''g''}}}}. This measure cannot be expressed as a functional multiplying the {{math|{{mathcal|D}}''x''}} measure because they belong to entirely different classes.