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Measurements of luminosity obtained using the ATLAS detector during early running of the Large Hadron Collider (LHC) at sqrt(s) = 7 TeV are presented. The luminosity is independently determined using several detectors and multiple algorithms, each having different acceptances, systematic uncertainties and sensitivity to background. The ratios of the luminosities obtained from these methods are monitored as a function of time and of mu, the average number of inelastic interactions per bunch crossing. Residual time- and mu-dependence between the methods is less than 2% for 0<mu<2.5. Absolute luminosity calibrations, performed using beam separation scans, have a common systematic uncertainty of +/-11, dominated by the measurement of the LHC beam currents. After calibration, the luminosities obtained from the different methods differ by at most +/-2%. The visible cross sections measured using the beam scans are compared to predictions obtained with the PYTHIA and PHOJET event generators and the ATLAS detector simulation.