Conservative, ae

Stream: maths

[Yury G. Kudryashov]

The notion of docs#MeasureTheory.Conservative depends on ae μ only. Does it make sense to consider this for other countably interection filters? E.g., what do we get for residual?

[Yury G. Kudryashov]

UPD: No, it also depends on the σ-algebra of measurable sets.

[Yury G. Kudryashov]

But it's about MeasurableSpace, not Measure.

[Yury G. Kudryashov]

Another related question: should we generalize docs#MeasureTheory.IsFundamentalDomain to any filter + EventuallyMeasurableSet?

[Yury G. Kudryashov]

@Felix Weilacher :up:

[Yury G. Kudryashov]

Also, should we rename docs#MeasureTheory.HasFundamentalDomain to IsDissipative?

[Yury G. Kudryashov]

... and what's the right definition of "conservative" for a group action?

[Felix Weilacher]

I certainly agree that Conservative depends only on the filter of conull sets.

Would it make sense to have a class of CountableInterFilters which arise as ae m for some suitably nice measure m on fixed MeasurableSpace? (I.e, as is discussed here) Certainly in informal math people are often thinking only of these filters, and don't really care which equivalent measure is chosen.

Anyways, the notion certainly makes sense for any Filter on a Measurable Space. For residual, for maps with enough continuity on nice enough spaces, it will be the same as saying every nonempty open set has nonempty intersection with one of its iterates.

[Felix Weilacher]

Is there not a fundamental-domain definition which doesn't assume any measurable structure?