我們簡短介紹均勻分佈模一數列的一些理論和發展，回顧了一些基本概念和重要理論，然後推了一個能夠幫助我們判斷均勻分佈模一的數列。

其次，我們討論了一個絕對連續函數，它的導數的平均值趨於無理數，並且我們將這個函數在正數上的所有值收集為一個數列。我們證明這個數列是均勻分佈模一的。

最後，我們討論均勻分佈模一相關的應用，簡短的介紹正規數，猜測一些數是否為正規。

In this thesis, we briefly introduce some theories and developments of
uniform distribution of sequences modulo 1, recall some basic concepts and important theories, and then we generalize a theorem which can help us determine uniform distribution of sequences.

Secondly, we discuss an absolutely continuous function with average
value of its derivative tends to an irrational number, and we collect all values of this function on positive numbers as a sequence. We prove that this sequence is uniformly distributed modulo 1.

Finally, we discuss a topic related to uniformly distributed modulo 1 and introduce normal number. We also guess some certain numbers are normal.

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