The concept of computerized tomography (CT) has been utilized by multi-phase fluid-flow experimentalists to measure cross-sectional void-fraction distributions in a non-invasive manner. This technique involves, in general, multiple solutions due to the nature of the tomographic inversion mathematics. Picking the (physically) right solution from a set of (mathematically) correct solutions requires a comprehensive understanding of various errors inherent in the tomographic inversion formula. The Kanpur error theorems, based on Sobolev space analysis, are used in a mercury-nitrogen two-phase flow experiment to make the correct choice. This approach provides the researchers with a way of estimating the accuracy of CT measurements for multi-phase flows in general, which is not possible otherwise.