Please note that the content of this book primarily consists of articles available from Wikipedia or other free sources online. In mathematics, the Vitali–Hahn–Saks theorem states that given n for each integer n >0, a countably additive function defined on a fixed sigma-algebra , with values in a given Banach space B. Mathematics is the study of quantity, structure, space, and change. Mathematicians seek out patterns, formulate new conjectures, and establish truth by rigorous deduction from appropriately chosen axioms and definitions. There is debate over whether mathematical objects such as numbers and points exist naturally or are human creations. The mathematician Benjamin Peirce called mathematics "the science that draws necessary conclusions".

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