If X is a Brownian motion, then for any α α ∈ ∈ ( 0 , 1 / 2 ) the field of local times L = ( L x ( t ) ) x ∈ ∈ R , t ≥ ≥ 0 has a modification which is a.s. Hölder continuous in x with exponent α α , uniformly for bounded x and t . In general, L has a modification that is a.s. continuous in t and càdlàg in x .