Can there be fields inside fields in Ingress?

You can create bigger fields around smaller one (until the links do not cross). The MU will also be credited twice (even with fields belonging to different factions)

According to this documentation:

If one control region fully encloses another control region, both regions get credit for all the mind units they enclose.

Edit :

Rules about links and fields :

• links cannot cross, never : It would be bad. (Dr E. Spengler ;) ) (neither a green link can cross a blue link).
• you can create fields inside other fields, but only if you link some portals making the outer field to an inner portal (source). You can't make a field completely inside another...Yet you can make fields completely around other fields.

You now can create fields within fields: 1. Friendly portal inside existing friendly field. 2. Clear path to portal from at least two of the anchor points to the field. 3. Link from each anchor point that has a clear path to the portal.