How to define a Measure that is the product of an expression and a Measure?

variational formulation
1

I’m working with axisymmetric problems and I’m looking for a compact and less error prone way to write integrals in the form:

\int_\Omega (\cdot) 2\pi r\, dx

by defining a Measure:

dm = 2\pi r\, dx

Does UFL support this kind of definition?

As I did not find how to do it with UFL, I thought of defining the following class:

from ufl import Measure

class CompoundMeasure(Measure):
    def __init__(self,
                 integral_type,
                 detJ,
                 domain=None,
                 subdomain_id='everywhere',
                 metadata=None,
                 subdomain_data=None):
        super().__init__(integral_type,
                         domain=domain,
                         subdomain_id=subdomain_id,
                         metadata=metadata,
                         subdomain_data=subdomain_data)
        self.detJ = detJ
    
    def __rmul__(self, integrand):
        return super().__rmul__(integrand * self.detJ)

And then use it to define the Measure dm as follows:

(r, z) = SpatialCoordinate(mesh)
detJ = 2*pi*r
dm = CompoundMeasure('cell', detJ)

Would it work or would it break any FEniCS feature?