Titlebook: Measure Theory; Paul R. Halmos Textbook 1950 Springer Science+Business Media New York 1950 Hilbert space.integration.measure.measure theor

机构

OGLE

适宜

Measurable Functions,(X,S) for .. It is customary to call a subset . of .. if and only if it belongs to the σ-ring .. This terminology is not meant to indicate that . is the σ-ring of all µ*-measurable sets with respect to some outer measure µ*, nor even that a non trivial measure is or may be defined on ..

Forage饲料

厚脸皮

Product Spaces, the sequel uses the words and concepts suggested by this example. Thus, for instance, if . ⊂ . and . ⊂ Y, we shall call the set . = . × . (a subset . × .) a . and we shall refer to the component sets . and . as its . (Observe that our usage here differs from the classical terminology which speaks of rectangles only if the sides are intervals.)

ingenue

Forehead-Lift

Measure and Topology in Groups, the assertion that not only is the measure determined by the topology, but that, conversely, all topological concepts may be described in measure theoretic terms. Throughout this section we shall assume that

Brochure

Sets and Classes,mbol in a special context, will be denoted by .. The elements of . will be called .; the set . will be referred to as the ., or the . or . space, under consideration. The purpose of this introductory chapter is to define the basic concepts of the theory of sets, and to state the principal results which will be used constantly in what follows.

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