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We observed with the camera FORS1 on the VLT (UT1, ANTU) 50 randomly selected fields and analyzed the cosmic shear inside circular apertures with diameter ranging from 0.5 to 5.0 arcmin. The images were obtained in optimal conditions using the Service Observing proposed by ESO on the VLT, which enabled us to a well-defined and homogeneous set of data. The 50 fields cover a 0.64 square-degrees area spread over more than 1000 square-degrees obtain which provides a sample ideal for minimizing the cosmic variance. Using the same techniques as in Van Waerbeke et al., we measured the cosmic shear signal and investigated the systematics of the VLT sample. We find a significant excess of correlations between galaxy ellipticities on those angular scales. The amplitude and the shape of the correlation as function of angular scale are remarkably similar to those reported so far. Using our combined VLT and CFHT data and adding the results published by other teams we put the first joint constraints on Omega0 and sigma8 using cosmic shear surveys. From a deduced average of the redshift of the sources the combined data are consistent with sigma8 ~= 0.59 +0.03-0.03 Omega0-0.47 (for a CDM power spectrum and Gamma=0.21), in excellent agreement with the cosmological constraints obtained from the local cluster abundance. This is consistent with theoretical expectations if the density field grew from initial Gaussian conditions

Cosmic shear analysis in 50 uncorrelated VLT fields. Implications for $\Omega_0$, $\sigma_8$