Homework 1 Solutions
نویسنده
چکیده
Exercise [1.1.13] (a) Let G = ⋂ α Fα, with each Fα a σ-algebra. Since Fα a σ-algebra, we have that Ω ∈ Fα, and as this applies for all α, it follows that Ω ∈ G. Suppose now that A ∈ G. That is, A ∈ Fα for all α. Since each Fα is a σ-algebra, it follows that A ∈ Fα for all α, and hence A ∈ G. Similarly, let A = ⋃ iAi for some countable collection A1, A2, . . . of elements of G. By definition of G, necessarily Ai ∈ Fα for all i and every α. Since Fα is a σ-algebra, we deduce that A ∈ Fα, and as this applies for all α, it follows that A ∈ G.
منابع مشابه
Effects of Annotations and Homework on Learning Achievement: An Empirical Study of Scratch Programming Pedagogy
In Taiwan elementary schools, Scratch programming has been taught for more than four years. Previous studies have shown that personal annotations is a useful learning method that improve learning performance. An annotation-based Scratch programming (ASP) system provides for the creation, share, and review of annotations and homework solutions in the interface of Scratch programming. In addition...
متن کاملOutlines of Solutions to Selected Homework Problems
This handout contains solutions and hints to solutions for many of the STA 6505 homework exercises from Categorical Data Analysis, second edition, by Alan Agresti (John Wiley, & Sons, 2002). It should not be distributed elsewhere without permission of the author. Additional solutions for odd-numbered exercises are available at the website for the text, http://www.stat.ufl.edu/∼aa/cda/cda.html. ...
متن کاملCommunication Technology Laboratory Fundamentals of Wireless Communications Homework 1 Solutions Problem 1 Identification of Ltv Systems
Fundamentals of Wireless Communications Homework 1 Solutions Handout date: April 1, 2014 Problem 1 Identification of LTV Systems 1. Suppose x stably identifiesQ. ForH1, H2 ∈ QwithH1x = H2xwe have 0 = H1x−H2x = (H1 −H2)x sinceH1, H2 are linear operators. Moreover,H1 −H2 ∈ Q. Since x stably identifiesQ, α‖H1 −H2‖H ≤ ‖(H1 −H2)x‖ = 0 with α > 0, which implies thatH1 −H2 = 0, i.e.,H1 = H2. 2. We sta...
متن کاملذخیره در منابع من
با ذخیره ی این منبع در منابع من، دسترسی به آن را برای استفاده های بعدی آسان تر کنید
عنوان ژورنال:
دوره شماره
صفحات -
تاریخ انتشار 2017