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We have utilized the BATSE--measured gamma--ray burst intensity distribution in conjunction with the general properties satisfied by integral moments to constrain significantly the permissable range of luminosities from which the observed gamma--ray bursts must be drawn. The constraints are independent of the functional form of the burst radial distribution. Given a distance independent luminosity function, the range of luminosity from which 80$\%$ of the observed gamma--ray bursts must be drawn may not exceed $\sim$6.5, with a 3--sigma upper limit of approximately 12. The finding that a substantial majority of bursts are passable standard--candles has important ramifications for many burst production models.
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