Ideal gas except for the specification of these constants. The results of the quantum Boltzmann gas are used in a number of cases including the Sackur–Tetrode equation for the entropy of an ideal gas and the Saha ionization equation for a weakly ionized plasma. The classical thermodynamic properties of an ideal gas can be described by two equations of state: The ideal gas law is the equation of state for an ideal gas, given by: where The ideal gas law is an extension of experimentally discovered gas laws. It can also be derived from microscopic considerations. Real fluids at low density and
Positive and negative sets nonnegative (resp. nonpositive) everywhere on "A". Of course, if μ is a nonnegative measure, every element of Σ is a positive set for μ. In the light of Radon–Nikodym theorem, if ν is a σ-finite positive measure such that |μ| « ν, a set "A" is a positive set for μ if and only if the Radon–Nikodym derivative dμ/dν is nonnegative ν-almost everywhere on "A". Similarly, a negative set is a set where dμ/dν ≤ 0 ν-almost everywhere. It follows from the definition that every measurable subset of a positive or negative set is also positive or negative. Also, the