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 there is a partition of "X" into a positive and a negative set; such a partition ("P","N") is unique up to μ-null sets, and is called a "Hahn decomposition" of the signed measure μ. Given a Hahn decomposition ("P","N") of "X", it is easy to show that "A" ⊆ "X" is a positive set if and only if "A" differs from a subset of "P" by a μ-null set; equivalently, if "A"−"P" is μ-null. The same is true for negative sets, if "N" is used instead of "P". Positive and negative sets In measure theory, given a measurable space ("X",Σ)