# Category Archives: 2017 Math

## Definition of Locally Convex Topological Spaces

Locally convex topological space의 정의는 크게 두 가지가 있다. 하나는 Definition A. A linear topological space is called a locally convex linear topological space if any of its open sets containing contains a convex, balanced and absorbing open set. 이고 또 다른 하나는 Definition B. A linear topological space is called a locally convex linear… Read More »

## Construction of Bergman kernel, evaluation of Bergman kernel

In this note, first we construct a Bergman kernel of simply connected smooth bounded domain in . Next, we evaluate the Bergman kernel when the domain is a unit disc. Finally, we introduce Bergman metirc on a complex manifold. 1. Construction of Bergman kernel Let be a bounded, simply connected and smooth domain in .… Read More »

## Marcinkiewicz-Zygmund’s SLLN

First, we present well-known Khintchine-Kolmogorov Theorem. Theorem (Khintchine-Kolmogorov). Let be independent random variables with finite expectation. If , then converges a.e. Now we present the Marcinkiewicz-Zygmund theorem which is our object of this article. Theorem (Marcinkiewicz-Zygmund Theorem). Suppose that are i.i.d with for some . Then     where     Proof. Set    … Read More »