List questions from examples-counterexamples

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If $f$ is Lebesgue measurable on $[0,1]$ then there exists a Borel measurable function $g$ such that $f=g$ a.e.?

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Two variable limits via paths - are there pathalogical examples?

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List Question

Topologist's Sine Curve not a regular submanifold of $\mathbb{R^2}$?

$\int f_k\to 0 $ but $f_k $ does not converge to $0 $ ae, where $ f_k $ is defined in $[0, 1] $

If $f$ is Lebesgue measurable on $[0,1]$ then there exists a Borel measurable function $g$ such that $f=g$ a.e.?

Examples of uncountable sets with zero Lebesgue measure

Two variable limits via paths - are there pathalogical examples?

Does Self Duality imply Hamiltonicity?

Objects with a "Homogeneity Principle"

Both atoms and co-atoms in a lattice

List of proofs of non-trivial theorems which were unnoticed to be wrong for at least a few years

Mutually densely-embedded non-homeomorphic topological spaces

Possible to make a flow that forms horseshoes on a 2-dimensional manifold?

Example of a singular element which is not a topological divisor of zero

Trace zero matrix that can't be written as $AB - BA$?

How to come up with a counter example in linear algebra

What are some examples of infinite dimensional vector spaces?

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