An E145 flight crew encountered an air/ground switch failure after takeoff and elected to continue to their destination.

Narrative

The LG AIR/GND FAIL EICAS caution illuminated right after gear was selected UP after takeoff. After running the after takeoff checklist; we consulted the QRH. We contacted dispatch and maintenance and asked them if they wanted us to return or proceed to our destination. They indicated that they preferred for us to continue unless we had any objections. Our weight at takeoff was 46;443 LBS and if we returned we would have had to perform an overweight landing with a chance of having degraded braking; no spoilers; no nose-wheel steering; and possibly no ground idle. If we continued; there was a chance that we may encounter icing conditions at our destination increasing our un-factored landing distance and possibly have degraded anti-icing capabilities. Having seen this situation before; I was confident that it was just a bad indication and that our systems would operate normally on the ground. We elected to continue and asked dispatch to figure out our un-factored flaps 45 landing distance as well as to search for a possible alternate airport outside of the current weather system that was affecting our destination and alternate airport. We had 1;000 LBS contingency fuel and 999 LBS of planned burn to our original alternate. Dispatch suggested an alternate that would allow us to remain clear of icing conditions and had a 10;000 FT runway. We did not declare an emergency as we did not need any priority handling. We instead notified ATC that we would be conducting a precautionary landing and would like CFR in position as a precaution only. We never encountered any icing conditions and landed. The brakes worked fine; the spoilers deployed; ground idle was available and the nose wheel steering operated normally. We taxied to our gate on our own power without further incident. The discrepancy was entered in the log once at the gate.