Real Analysis

Welcome to the "Real Analysis" category on Questions LLC! This is the perfect place for those seeking a deeper understanding of the principles and concepts of real analysis. Here, you will find a diverse range of questions related to functions, sequences, limits, continuity, differentiation, integration, and much more. Whether you are a student studying mathematics, an academic researcher, or simply an individual with a curious mind, this category is designed to provide you with insightful answers and foster discussions on the intricacies of real analysis. So, dive in, explore the questions, and join the community in unraveling the complexities of this fascinating branch of mathematics!

Questions (11)

Question:If m*(E) = 0, show that E is Lebesuge measurable, where m*(E) denote the Lebesgue Outer Measure of E. ===============
1. 1 answer
2. asked by Ashley
3. 90 views
definiton: A set S subsect of real number,sequence {Xn} is called bounded if there is a number M such that |X|≤ M for all x
1. 4 answers
2. asked by Lucy
3. 624 views
Consider the subsets of R defined as follows: An is the interval (0,1/n) for all natural numbers. Show that:U (union) n=1 to
1. 1 answer
2. asked by Lola
3. 503 views
Let {X_n} be a sequence of real numbers that is bounded above by M and such that X_n-->x Prove that x<=M
1. 1 answer
2. asked by Ashley
3. 383 views
On the real line, define d (x, y ) = sqrt(abs(x − y)) . Prove that d satisfies the axioms of ametric.
1. 1 answer
2. asked by Ashley
3. 349 views
Let a,b exist in the reals with a<b.(i) for the open interval E=(a,b), prove that infE=a and supE=b. (ii) for the closed
1. 3 answers
2. asked by Ashley
3. 421 views
Prove:Let a,b exist in the reals with a<b, (i) For the open interval E=(a,b) prove that the inf E=a and sup E=b (ii) for the
1. 2 answers
2. asked by Ashley
3. 511 views
Let S be a non-empty subset of the real numbers that is bounded below. Define −Sby −S = {− x | x ∈S }. Prove: (i) −S
1. 1 answer
2. asked by Ashley
3. 499 views
Suppose that a set S is bounded above. Let r be any real number and t be any positive real number.Let T = {r + tx : x e S}. Show
1. 1 answer
2. asked by MATH HELP HELPPP
3. 357 views
Prove that the Least Upper Bound Property holds for ℝ if and only if the Greatest Lower Bound Property holds for ℝ.
1. 1 answer
2. asked by sara
3. 957 views
Continuous vs. Discrete: Finding Domain and Range ReviewWe will have to determine and write domain and range differently
1. 1 answer
2. asked anonymously
3. 23 views