# Timewise-average function

From Diffgeom

## Definition

Let be a differential manifold equipped with a measure over which we can integrate.

Let be any continuous function. Then the timewise-average function of is a map defined by:

For instance, the above notion makes sense if we embed the manifold in Euclidean space and look at the induced measure, or in a Riemannian manifold where we take the naturally induced measure.