American Electronic with rechargable UK battery

this might end up being a dumb question, but here goes....

rather than lug my voltage converter with me on my trips to europe, i thought i would just buy an additional digital camera battery instead.  but then i got to thinking.....

1) is a rechargeable Li-Ion battery bought in the UK going to work in my US digital camera? 
2) will the Li-Ion UK rechargeable battery charge on my US charging dock?

anyone have any thoughts on this?

There's no inherent difference between U.S. and U.K. batteries, other than branding and the fact that some have different manufacturers' codes. 

The charger units for both U.S. power (120V 60Hz) and U.K. power (240V 50Hz)  both convert to the same sort of current which is needed to charge the battery, so the battery neither knows nor cares about the power source.

So long as you obtain the correct type of battery for your camera, therefore, the answers are:

#1.  It will work in the U.S. camera just fine.

#2.  It will charge on your U.S. charger properly.

And, not asked, but also

#3.  The U.S. battery will charge perfectly well in the equivalent U.K. charger if you buy one.

excellent!!  thanks paul!!  i appreciate it!