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**Question about Landau: Definition of "Number of states with energy" in an interval**

Hey! I am currently reading Landau's Statistical Physics Part 1, and in Paragraph 7 ("Entropy") I am struggling with a definition.

Right before Equation (7.1) he gives the "required number of states with energy between [itex]E[/itex] and [itex]E+\mathrm{d}E[/itex]" as:

[tex]\frac{\mathrm{d}\Gamma(E)}{\mathrm{d}E} \mathrm{d}E[/tex]

I don't understand this equation. Am I supposed to understand [itex]\Gamma(E)[/itex] as a continuous function, and therefore [itex]\frac{\mathrm{d}\Gamma(E)}{\mathrm{d}E}[/itex] as a derivative?

Furthermore, how is the energy probability distribution

[tex]W(E) = \frac{\mathrm{d}\Gamma(E)}{\mathrm{d}E} w(E)[/tex]

different from [itex]w(E)[/itex]. Isn't [itex]w(E)[/itex] kind of a probability distribution by itself?