This paper presents an analysis of the inclusive properties of diffractive deep inelastic scattering events produced in ep interactions at HERA. The events are characterised by a rapidity gap between the outgoing proton system and the remaining hadronic system. Inclusive distributions are presented and compared with Monte Carlo models for diffractive processes. The data are consistent with models where the pomeron structure function has a hard and a soft contribution. The diffractive structure function is measured as a function of x(p), the momentum fraction lost by the proton, of beta, the momentum fraction of the struck quark with respect to x(p), and of Q(2) in the range 6.3 10(-4) < x(p) < 10(-2), 0.1 < .beta < 0.8 and 8 < Q(2) < 100 GeV2. The x(p) dependence is consistent with the form (1/x(p))(alpha) where alpha = 1.30 +/- 0.08 (stat)(-0.14)(+0.08) (sys) in all bins of beta and Q(2). In the measured Q(2) range, the diffractive structure function approximately scales with Q(2) at fixed beta. In an Ingelman-Schlein type model where commonly used pomeron flux factor normalisations are assumed, it is found that the quarks within the pomeron do not saturate the momentum sum rule.
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