Integral of Real-Valued Measurable Function1
نویسندگان
چکیده
منابع مشابه
Integral of Real-Valued Measurable Function
For simplicity, we follow the rules: X denotes a non empty set, Y denotes a set, S denotes a σ-field of subsets of X, F denotes a function from N into S, f , g denote partial functions from X to R, A, B denote elements of S, r, s denote real numbers, a denotes a real number, and n denotes a natural number. Let X be a non empty set, let f be a partial function from X to R, and let a be a real nu...
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One can prove the following propositions: (1) For all extended real numbers x, y holds |x− y| = |y − x|. (2) For all extended real numbers x, y holds y − x ≤ |x− y|. (3) Let x, y be extended real numbers and e be a real number. Suppose |x − y| < e and x 6= +∞ or y 6= +∞ but x 6= −∞ or y 6= −∞. Then x 6= +∞ and x 6= −∞ and y 6= +∞ and y 6= −∞. (4) For all extended real numbers x, y such that for...
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ژورنال
عنوان ژورنال: Formalized Mathematics
سال: 2006
ISSN: 1898-9934,1426-2630
DOI: 10.2478/v10037-006-0018-8