We prove that if t {mapping} u(t) ∈ BV (?) is the entropy solution to a N × N strictly hyperbolic system of conservation laws with genuinely nonlinear characteristic fields u _t + f(u) _x = 0, then up to a countable set of times {t _n} _(n∈?) the function u(t) is in SBV, i.e. its distributional derivative u _x is a measure with no Cantorian part. The proof is based on the decomposition of u _x(t) into waves belonging to the characteristic families, and the balance of the continuous/jump part of the measures v i in regions bounded by characteristics. To this aim, a new interaction measure μ _(i,jump) is introduced, controlling the creation of atoms in the measure v _i(t). The main argument of the proof is that for all t where the Cantorian part of v _i is not 0, either the Glimm functional has a downward jump, or there is a cancellation of waves or the measure μ _(i,jump) is positive.
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