The extent to which the current measured by all four beams is the same. A key assumption of all ADCP processing is that the currents are horizontally homogeneous across the four beams. This assumption is checked for each measurement by using the error velocity measurement.
The assumption that, on the large-scale, matter is uniformly spread throughout the universe.
The situation in which the standard deviation of the dependent (Y) variable is the same, regardless of the value of the independent (X) variable; an assumption in ANOVA and regression.