Study Of The Borel Measures & Analysis On Share Price's Fluctuation

" Anomaly " geometrical objects that appear in the nature such as the bank of clouds, the outline of mountain, snowflake, the boundary of coast are all difficult to describe with the straight line, smooth curve, smooth surface of classic geometry. But gathering of these anomalies can better describe many natural phenomena.In nineteen eighties fractal geometry founded by B.B.Mandelbrot provided thoughts, methods and techniques to study this anomaly geometry. Specially in recent years, this newly arisen subject reach large achievement in mathematics, physics, chemistry, biology, medical science, geology etc. At the same time, the large quantity of problems questioned by different courses stimulated the fractal geometry development.Measures have a central place in fractal geometry. They are not only a major tool in the mathematics of fractal, but also, measures may exhibit fractal features which may be studied in their own right. Basically, a measure is a way of an ascribing a numerical size to sets. In this paper, we mainly talk about an interesting measure in symbolic space which is defined by a very useful method of repeated subdivision. At last we will show that such a measure is a Borel regular measure. (In the first place, we show that it is a (outer) measure. In the second place, it is a Borel measure. Finally, it is a Borel regular measure.) Besides, we will still explain that an invariant measure produced by Iterated Function System satisfying the strong separation condition is a special example of it.There is no consensus about the dymamics of the stock market variations till now. The classical financial models have regarded market shift as a random process, and argued that the stock market cannot be predicted. But recently, more and more scientists find that economic systems are not strictly simple random walk as a time series. In the third section, we firstly review some definitions and notations, such as the coarse multifractal spectrum fc and the Hausdorffmultifractal spectrum fH etc. Secondly, we research some share price by the approximate multifractal formalism and calculate the multifractal spectrum fα of some share price by the method of box-counting. At last, we use some datas of the closing price in HuShen stock validating that not only the variation of the share price can be described by fα, but also the fluctuation of it can be predicted by Δf.