About the Book
Please note that the content of this book primarily consists of articles available from Wikipedia or other free sources online. Pages: 40. Chapters: Lebesgue measure, Borel measure, Haar measure, Complete measure, Probability measure, Secondary measure, Radon measure, Vector measure, Harmonic measure, Signed measure, Hausdorff measure, Jordan measure, Cylinder set measure, Gibbs measure, Outer measure, Tangent measure, Resource bounded measure, Projection-valued measure, Spherical measure, Gaussian measure, Empirical measure, Complex measure, Pushforward measure, -finite measure, Green measure, Dirac measure, Invariant measure, Carleson measure, Minkowski content, Discrete measure, Product measure, Inner measure, Metric outer measure, Strictly positive measure, Maximising measure, Pre-measure, Regular measure, Singular measure, Transverse measure, Counting measure, Quasi-invariant measure, Trivial measure, Inner regular measure, Uniformly distributed measure, Perfect measure, Random measure, Locally finite measure, Borel regular measure, Idempotent measure, Logarithmically concave measure, Banach measure, Saturated measure, Baire measure. Excerpt: In mathematical analysis, a measure on a set is a systematic way to assign to each suitable subset a number, intuitively interpreted as the size of the subset. In this sense, a measure is a generalization of the concepts of length, area, volume. A particularly important example is the Lebesgue measure on a Euclidean space, which assigns the conventional length, area and volume of Euclidean geometry to suitable subsets of the n-dimensional Euclidean space R. For instance, the Lebesgue measure of the interval in the real numbers is its length in the everyday sense of the word, specifically 1. To qualify as a measure (see Definition below), a function that assigns a non-negative real number or + to a set's subsets must satisfy a few conditions. One important condition is countable additivity. This condition states that ...
