دانلود کتاب تئوری تغییر ناپذیر اندازه گیری و شیفت ترکیبی مقیاس های زمانی و کاربردها

Measure theory was initiated at the beginning of the twentieth century and “measure” is an important notion in analyzing the subsets of Euclidian spaces. In 1989, E. Borel first established a measure theory on subsets of the real numbers known as Borel sets, and Lebesgue measure was introduced by H. Lebesgue in 1902 and the related integral based on measure theory is more comprehensive than the Riemann integral. In fact, the notion of measure and its significance widely generalize the classical definitions of “length” and “area” in Euclidian spaces. In 1918, the concept of outer measures was introduced and studied by C. Carathéodory. Since then, measure theory and the calculus theory based on it were developed rapidly in the field of pure and applied mathematics.