Direct calculation of fluctuation formulae in the microcanonical ensemble

We present simple derivations of the classical microcanonical ensemble formulae for fluctuations which involve the kinetic energy and microscopic pressure function. The new derivations, which confirm earlier results of Lebowitz et al. [1] and Cheung [2], proceed in a direct way from basic microcanonical ensemble theory without recourse to fluctuation expressions of other ensemble theories. The method developed is applicable to shell ensembles in general.