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Here I summarize some tools for proof of the Riesz representation theorem. They are the limit of inequality of sequence and …

This is a note of real and complex analysis chapter 2. Chapter 2 is about measures. The measure already defined in chapter 1. In …

This is a note for Rudin’s real and complex analysis chapter 1. The key concepts are \(\sigma\)-algebra, measure (\(\mu\)) zero, and …

The compact is a property of space. In a nutshell, if space is compact, we can treat the space be a finite because space has a finite …

Differential equation solution is infinite function series. The infinite function series can be a sort of linear combination of …

A sequence can be defined as a function on the domain of natural number like \(1, 1/2, 1/3 ... 1/n\). This sequence approach to the 0, …

The studying sometimes starts with learning of boring preceding concepts. The highlight comes later. In history, the highlight concepts …

The reproducing kernel hilbert space (RKHS) was my motivation to study analysis. The hilbert space is a orthogonal normed vector space. …