一. 內容：
1. Hausdorff dimensional measures; n-dimensional lebesgue measure and transformation of integrals.
2. Decomposition and Differentiation of Measures. Differentiation on $R^n$ and functions of a real variable (functions of bounded variation and convex functions).
3. Analysis on $L^P$-spaces-Distribution function, weak $L^P$-functions and interpolation of $L^P$-spaces.
4. Sobolev spaces and Variational methods.
5. Miscellaneous topics in Fourier Analysis and Probability.

二. 參考書（教科書）：
1. Follard, G. B. Real Analysis, Wiley 1984.
2. Wheaden, R. L. & Zygmund, A. Measure and Integration, Marcel Dekker, 1977.
3. Rogers, C. A. Hausdorff Measure, Cambridge U. Press 1970.

三. 成績評量方式：
習 題 40﹪
期中考 30﹪
期末考 30﹪

四. 其他：