I am wondering if we can assume the following if your function $f$ is $K-$lipschitz: $$\delta(f(A),f(B)) \leq K*\delta(A,B),$$ where we use the definition: $$\delta(A,B) = \inf\{\epsilon \geq 0\,|\ A \subseteq B_\epsilon \text{ and } B \subseteq A_\epsilon\}.$$ I have troubles to see how one should get this.. Any help would be great!
2026-03-25 10:59:36.1774436376
Lipschitz function and Hausdorff distance
29 Views Asked by Bumbble Comm https://math.techqa.club/user/bumbble-comm/detail AtRelated Questions in ANALYSIS
- Analytical solution of a nonlinear ordinary differential equation
- Finding radius of convergence $\sum _{n=0}^{}(2+(-1)^n)^nz^n$
- Show that $d:\mathbb{C}\times\mathbb{C}\rightarrow[0,\infty[$ is a metric on $\mathbb{C}$.
- conformal mapping and rational function
- What are the functions satisfying $f\left(2\sum_{i=0}^{\infty}\frac{a_i}{3^i}\right)=\sum_{i=0}^{\infty}\frac{a_i}{2^i}$
- Proving whether function-series $f_n(x) = \frac{(-1)^nx}n$
- Elementary question on continuity and locally square integrability of a function
- Proving smoothness for a sequence of functions.
- How to prove that $E_P(\frac{dQ}{dP}|\mathcal{G})$ is not equal to $0$
- Integral of ratio of polynomial
Related Questions in LIPSCHITZ-FUNCTIONS
- Is a Lipschitz function differentiable?
- Equivalence for a reversed Lipschitz-type condition
- Compact sets in uniform norm
- Does locally Lipschitz imply Lipschitz on closed balls?
- An upper bound for $\|2 \nabla f(x) - \nabla f(y)\|$ in terms of $\|x-y\|$ if the gradient is $L$-Lipschitz
- Nowhere-differentiable Lipschitz-continuous function
- How to prove the following function is not Lipschitz continuous?
- Question on Lipschitz continuity
- Is the Borel isomorphic interchanging-digit map a k-Lipschitz map?
- Could lower semicontinuous functions have Lipschitz constant?
Related Questions in HAUSDORFF-DISTANCE
- Bounds on the difference of sups in terms of the Hausdorff distance between feasible regions
- Hausdorff distance between two set of finite points
- Hausdorff distance, Translation and Intersection
- How to properly read Hausdorff Metric?
- Convergence properties in a Hausdorff space that is a ring
- Continuity of the kernel of bounded operators under perturbation
- Some questions about Hausdorff distance
- A way to prove that Hausdorff distance is complete
- Equivalent geodesic rays
- A bound for the Hausdorff distance
Trending Questions
- Induction on the number of equations
- How to convince a math teacher of this simple and obvious fact?
- Find $E[XY|Y+Z=1 ]$
- Refuting the Anti-Cantor Cranks
- What are imaginary numbers?
- Determine the adjoint of $\tilde Q(x)$ for $\tilde Q(x)u:=(Qu)(x)$ where $Q:U→L^2(Ω,ℝ^d$ is a Hilbert-Schmidt operator and $U$ is a Hilbert space
- Why does this innovative method of subtraction from a third grader always work?
- How do we know that the number $1$ is not equal to the number $-1$?
- What are the Implications of having VΩ as a model for a theory?
- Defining a Galois Field based on primitive element versus polynomial?
- Can't find the relationship between two columns of numbers. Please Help
- Is computer science a branch of mathematics?
- Is there a bijection of $\mathbb{R}^n$ with itself such that the forward map is connected but the inverse is not?
- Identification of a quadrilateral as a trapezoid, rectangle, or square
- Generator of inertia group in function field extension
Popular # Hahtags
second-order-logic
numerical-methods
puzzle
logic
probability
number-theory
winding-number
real-analysis
integration
calculus
complex-analysis
sequences-and-series
proof-writing
set-theory
functions
homotopy-theory
elementary-number-theory
ordinary-differential-equations
circles
derivatives
game-theory
definite-integrals
elementary-set-theory
limits
multivariable-calculus
geometry
algebraic-number-theory
proof-verification
partial-derivative
algebra-precalculus
Popular Questions
- What is the integral of 1/x?
- How many squares actually ARE in this picture? Is this a trick question with no right answer?
- Is a matrix multiplied with its transpose something special?
- What is the difference between independent and mutually exclusive events?
- Visually stunning math concepts which are easy to explain
- taylor series of $\ln(1+x)$?
- How to tell if a set of vectors spans a space?
- Calculus question taking derivative to find horizontal tangent line
- How to determine if a function is one-to-one?
- Determine if vectors are linearly independent
- What does it mean to have a determinant equal to zero?
- Is this Batman equation for real?
- How to find perpendicular vector to another vector?
- How to find mean and median from histogram
- How many sides does a circle have?