The Hedges Inn will not be allowed to hold outdoor events, even in tents, the East Hampton Village Zoning Board of Appeals decided on Friday. The decision corroborates opinions of the village administrator and building inspector, who, in March, denied four permits for the inn, a frequent wedding venue, on the grounds that outdoor dining is not a permitted use of the pre-existing, nonconforming commercial property, which is in a residential zone. The pertinent village law took effect on Oct. 1.