We use simulated images of star-forming regions to explore the effects of various image acquisition techniques on the derived clump mass function. In particular, we focus on the effects of finite image angular resolution, the presence of noise, and spatial filtering. We find that, even when the image has been so heavily degraded with added noise and lowered angular resolution that the clumps it contains clearly no longer correspond to pre-stellar cores, still the clump mass function is typically consistent with the stellar initial mass function within their mutual uncertainties. We explain this result by suggesting that noise, source blending, and spatial filtering all randomly perturb the clump masses, biasing the mass function toward a lognormal form whose high-mass end mimics a Salpeter power law. We argue that this is a consequence of the central limit theorem and that it strongly limits our ability to accurately measure the true mass function of the clumps. We support this conclusion by showing that the characteristic mass scale of the clump mass function, represented by the "break mass," scales as a simple function of the angular resolution of the image from which the clump mass function is derived. This strongly constrains our ability to use the clump mass function to derive a star formation efficiency. We discuss the potential and limitations of the current and next generation of instruments for measuring the clump mass function.
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