Transports for `WeightedMeasure`

[cscherrer]

Currently we have

transport_origin(ν::WeightedMeasure) = ν.base
to_origin(::WeightedMeasure, y) = y
from_origin(::WeightedMeasure, x) = x

Should this be

transport_origin(ν::WeightedMeasure) = transport_origin(ν.base)
to_origin(v::WeightedMeasure, y) = to_origin(v.base, y)
from_origin(v::WeightedMeasure, x) = from_origin(v.base, x)

?

It seems strange for wrapping an arbitrary measure with a weight to cause the transport mechanism to "give up".

[mschauer]

You may have to extend transport by creation and deletion of mass to make sense of weighted measures

[cscherrer]

Why is that?

[oschulz]

I guess the question is, do we allow transport between measures of unequal total mass? The current implementation does so, but maybe it actually goes to far? After all, the using the transport function as a pushforward on the "unweighted" measure would not return the original "weighted" measure. Maybe we should not treat measures that only differ in total mass as equivalent?

[cscherrer]

Hmm, yeah we do need to get to that mass interface.