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Results are presented on the inclusive production of isolated prompt photonsin deep inelastic scattering with a four-momentum transfer of $Q^2>4 GeV^2$.The cross sections are measured for the transverse momentum range of thephotons $3 < E_T^\gamma < 10 GeV$ and for the pseudorapidity range of thephotons $-1.2 < \eta^\gamma < 1.8$. They are measured differentially as afunction of $E_T^\gamma$ and $\eta^\gamma$. The results are compared with thepredictions of a leading order calculation, which is in reasonable agreementwith the inclusive measurement.Comment: To appear in the proceedings of 14th International Workshop on Deep  Inelastic Scattering (DIS 2006), Tsukuba, Japan, 20-24 Apr 200

INCLUSIVE PROMPT PHOTON PRODUCTION IN DEEP INELASTIC SCATTERING AT H1