Statistical Bochner Integral on Frechet Space

Probability theory including the Bochner integral is a very important part of modern mathematical concepts including the modern theory of probabilities, especially in the concept of mathematical expectation and dispersion. In this, study a statistical approach form of Bochner’s theory is given and extended, but some fundamental properties of statistical integral were previously studied in the Banach case. Our approach formulates an extended integration concept of Bochner. By using the statistical convergence on general locally convex space it is possible to obtain very similar results referring to the Frechet space type. From our results, some interesting comparable outputs to Banach space are carried out. At the end of our research, it is conducted that if a function “f” is Bochner integrable in the classic report then it is statistically Bochner integrable, but conversely, this is not true. Hence, the value of the extension of Bochner integration is a need and is the focus of our work. This extension is given by modifying the model published by Schvabik and Guoju. Mathematically it is substantiated that on the space of Frechet types the space of functions of statistical Bochner integrable is a Frechet space.