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We use 50 (candidate) background X-ray sources (AGN) in the LMC fieldobserved in ROSAT PSPC observations to derive the observed log N - log Srelation. We correct for the varying PSPC exposure and the absorption due tothe galactic and the LMC gas. We compare the observed log N - log S with atheoretical log N - log S of the soft extragalactic X-ray background (AGN and acluster of galaxy contribution). We find that the observed log N - log S has adeficiency with respect to the theoretical log N - log S. Factors which canaccount for such a deficiency are: (1) incompleteness of the selected AGN andcluster of galaxies sample, (2) deviation of the log N - log S in the LMC fieldfrom the log N - log S derived from a large sample of AGN in several fields,(3) existence of gas additional to the HI represented in the Parkes HI map ofthe LMC field. We investigate the likely contribution of these effects and findthat (1) a fraction of at most 30% of the background sources may not have beenfound in this analysis and may contribute to the observed deficiency. (2) Wecannot exclude a deviation of the log N - log S in the field of the LMC from atheoretical log N - log S, especially the cluster of galaxy contribution mayshow variations across the sky. (3) If LMC gas (restricted to >10^21 cm^-2columns) in addition to the HI represented in the Parkes map would beresponsible for the deficiency, then a factor of >0.3 (at 90% confidence) ofadditional gas would be required. This would equal a molecular mass fraction of>21%, which would be larger than, but within the uncertainties consistent witha molecular mass fraction of ~30% derived from CO observations (for columns>10^21 cm^-2).Comment: 14 pages, accepted for publication in A&A, March 22 200

ROSAT X-ray sources in the field of the LMC