Internationally, no problems if direct flight.
Domestic, from the United website,
"The Transportation Security Administration (TSA) allows each traveler to carry on liquids, gels and aerosols in containers of 3.4 ounces (100 mL) or less, inside a single quart-size (or liter-size) clear, sealable bag.
Passengers traveling internationally into the U.S. and connecting to another flight are allowed to have in their carry-on baggage liquids in excess of 3.4 ounces (100 mL) that were purchased as duty-free merchandise. This only applies to products purchased in duty-free stores, placed in an intact designated secure, tamper-evident bag, and successfully screened and cleared by TSA officers. Scanning may not be effective for liquids in opaque, ceramic, or metallic bottles, or other containers. Liquids that cannot be screened and cleared will not be allowed to remain in carry-on baggage. Customers may choose to place these items into checked baggage or throw them away."
To be safe, check with the specific airline for that domestic leg.
I know it's a different country, but one can't, for example, carry bottles of Scotch bought duty free in GLA onto London bound flights.