# Borel set

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## Borel set

[bȯ·rel ¦set]
(mathematics)
A member of the smallest σ-algebra containing the compact subsets of a topological space.
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kentucky derby star Borel set for dubai debut in hot competition
More in general, as we shall see in the next sections, if the boundary [partial derivative] A of a J-dimensional Borel set A [member of] [R.
Definition 2 (The class O) Let O be the class of Borel sets A of [R.
d-1] ([partial derivative]A); then it follows that this class of sets contains all Borel sets with (d-1)-rectifiable boundary (and so finite unions of sets with positive reach or with Lipschitz boundary, in particular).
there exists a constant C > 0 such that for any Borel set b of R, [MATHEMATICAL EXPRESSION NOT REPRODUCIBLE IN ASCII] where [MATHEMATICAL EXPRESSION NOT REPRODUCIBLE IN ASCII] denotes the norm in the Banach space B*.
For n [member of] Nand a Borel set b in R, put [[mu].
The next question we turn to is whether the distal flows form a Borel set.
This has the immediate corollaries that the distal flows of a given bounded rank form a Borel set and that the distal functions of a bounded rank form a Borel set.
k]) is a collection of Borel sets indexed by [Mathematical Expression Omitted] then "natural number quantification", which corresponds to countable unions and intersection, over this collection always yields a Borel set.
Namely, if [Mathematical Expression Omitted] for some Borel set E [subset] [C.
n-1](f(E)) = 0 for all Borel sets E [subset] [Delta][B.
The text covers sets and functions, Lebesgue measure, measurable sets, Borel sets, sets of measure zero, the integral, measurable functions, convergence theorems, convergence in mean, Fourier theory, calculus, change of variables, differentiation of integrals, integration of derivatives, and general measures.

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