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Jet production is studied in the Breit frame in deep-inelasticpositron-proton scattering over a large range of four-momentum transfers 5 <Q^2 < 15000 GeV^2 and transverse jet energies 7 < E_T < 60 GeV. The analysis isbased on data corresponding to an integrated luminosity of L_int \simeq 33pb^(-1) taken in the years 1995-1997 with the H1 detector at HERA at acenter-of-mass energy sqrt(s)=300 GeV. Dijet and inclusive jet cross sectionsare measured multi-differentially using k_perp and angular ordered jetalgorithms. The results are compared to the predictions of perturbative QCDcalculations in next-to-leading order in the strong coupling constantalphas.QCD fits are performed in which alphas and the gluon density in theproton are determined separately. The gluon density is found to be in goodagreement with results obtained in other analyses using data from differentprocesses. The strong coupling constant is determined to bealphas(MZ)=0.1186+-0.0059. In addition an analysis of the data in which bothalphas and the gluon density are determined simultaneously is presented.Comment: 44 pages, 19 figures, 5 table

Measurement and QCD analysis of jet cross sections in deep-inelastic positron-proton collisions at $\sqrt{s}$ of 300 GeV