The relationship between the residual porosity, linear optical loss coefficient, and sintering tem perature-time regime has been studied for Y 3 Al 5 O 12 :Nd 3+ (4 at %) laser ceramics. It is experimentally estab lished that the linear optical loss coefficient linearly depends on the magnitude of residual porosity. The slope efficiency of laser generation reached a value of 31% in ceramics with a residual porosity on a level of 0.0016 vol % that was obtained by reactive sintering at 1750°C for 12 h. The obtained results are important for optimization of the technology of Y 3 Al 5 O 12 :Nd 3+ laser ceramics.

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We develop a general method for the construction of a probability structure on the space ᑟ of random sets in R. For this purpose, by using the introduced notion of c-system, we prove a theorem on the unique extension of a finite measure from a c-system to the minimal c-algebra. The obtained structure of measurability enables one to determine probability distributions of the c-algebra of random events sufficient, e.g., for the so-called fractal dimensionality of random realizations to be considered as a measurable functional on ᑟ.