International Journal of Applied Research
Vol. 2, Issue 1, Part K (2016)
Interplay between measure theory and topology
Topology and measure theory are very closely related. Both are concerned with spaces equipped with certain algebras of sets (open sets, measurable sets) and classes of functions (continuous functions, measurable functions). Continuous functions (on reasonable spaces) are measurable, and (some) measures can be integrated to define continuous functions. To every topological space X one can associate the Borel σ-algebra, which is the σ-algebra generated by all open sets in X. In this paper we will prove that for locally compact Hausdorff space, ξ be any class of open sets which generates the topology of X, then the σ-ring generated by ξ contains every Baire sets and define a Baire measure on product spaces.
How to cite this article:
Parvinder Singh. Interplay between measure theory and topology. International Journal of Applied Research. 2016; 2(1): 727-734.