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Homework 3, Real Analysis 2

Due February 23 Probl For any two Cantor sets , as constructed in HW2, Problem 3, there exists a continuous, bijective and increasing function that maps surjectively onto . There exists a measurable function f and a continous function such that is non-measurable. Problem 2 Given a collection of sets , there exists a disjoint […]

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Tarea 3, Matemáticas discretas

Fecha de entrega: 23 de febrero Problema 1 Experimenta, haz una conjetura y demuestra, tanto por inducción como combinatóricamente, el valor de la suma Problema 2 Demuestra la identidad interpretando combinatóricamente los términos positivos y negativos. Problema 3 Demuestra combinatóricamente que Problema 4 ¿De cuántas formas puedes acodomodar 8 torres (iguales) en un tablero de […]

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Tarea 2, Matemáticas discretas

Fecha de entrega: 16 de febrero Problema 1 n niños y n niñas salen a bailar en parejas, ¿de cuántas formas pueden hacerlo? (Solo parejas niño-niña.) Problema 2 Demuestra combinatóricamente que  Problema 3 Ana tiene 10 pelotas. Primero, las separa en dos grupos (no necesariamente del mismo tamaño). En seguida, toma uno de los dos grupos, […]

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Homework 2, Real Analysis 2

Due February 16 Problem 1 Let with . For each , there exists an open interval I such that . If E is measurable, the difference set contains an open interval centered at the origin. Problem 2 Let C be the Cantor set. if and only if , where . The Cantor-Lebesgue function is defined on C by […]

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Homework 1, Real Analysis 2

Due February 9 Problem 1 The Cantor set is totally disconnected (for any there is between x and y) and perfect (compact and without isolated points). Problem 2 Let and If E is compact, The previous conclusion may be false for E closed and unbounded, or open and bounded. Problem 3 (Borel-Cantelli lemma) Let be a sequence of measurable sets […]

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