MAT 332E - Reel Analiz I

Dersin Amaçları

1. Düzlemde ve daha sonra genel ölçü kavramlarını vermek.
2. Riemann integrali genişlemesi olarak Lebesgue integralini vermek.
3. Lebesgue integralinin özelliklerini öğretmek ve bunları matematiksel problemlere uygulama becerisi
kazandırmak.

Dersin Tanımı

The concept of measure. Measurable sets on plane and R^n . Inner and outer measure functions. General
measure. The extension of measure function. Properties of measurable sets. Cantor and Borel sets.
Measurable functions. Lebesgue’s integral. The properties of Lebesgue’s integral. The notions of
convergence. Comparison of Lebesgue’s with Riemann’s integral. The theorems of Lebesgue, Fatou and
Levi. The measure of product. Lebesgue’s integral on product spaces. Fubini’s theorem.