A Foundation of $\sigma$-superadditive Measures -- a note on advancing Kalina measures -

The present paper attempts to modify the way of constructing a measure in the Alternative Set Theory setting originally devised by Martin Kalina. Introducing a system of cuts of rational numbers extended with some special ones, it is proved that the measure which is nondecreasing, nonnegative and “depending on the way of measurement” as same as Kalina’s, but exhibits $\sigma$-superadditivity is obtained.