Fatou's Lemma for Weakly Converging Probabilities

Fatou's lemma states under appropriate conditions that the integral of the lower limit of a sequence of functions is not greater than the lower limit of the integrals. This note describes similar inequalities when, instead of a single measure, the functions are integrated with respect to different measures that form a weakly convergent sequence

Special Aspects in Designing High - Frequency Betatron

The article is devoted to designing the high - frequency betatron. In high - frequency betatron most important problem is overheating of the elements of the body radiator unit. In an article some directions of solving this problem are shown