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Uniform Approximation of Continuous Functions by Nontrivial Simple Functions
Yu-Lin Chou
We prove that every nonnegative continuous real-valued function on a given compact metric space is the uniform limit of some increasing sequence of nonnegative simple functions bei…
A Remark on Lebesgue Criterion
Yu-Lin Chou
We remark a variant of the existence part of the fundamental theorem of calculus, which, together with the Lebesgue differentiation theorem, constitute a new proof that every Riema…
Some Remarks on Hausdorff Measurability of Lipschitz Images in Metric Spaces
Yu-Lin Chou
In this short note, we show that, in any given metric space, every Lipschitz open-map image of every subset of a given metric space whose boundary is Hausdorff-null is Hausdorff-me…
Generalization and New Proof for Almost Everywhere Convergence to Imply Local Convergence in Measure
Yu-Lin Chou
With a new proof approach we prove in a more general setting the classical convergence theorem that almost everywhere convergence of measurable functions on a finite measure space…
Fermat's Equation Has No Solution with Some Prime Components
Yu-Lin Chou
Within the scope of elementary number theory, we prove that, as the main result, if are integers such that at least one of is prime then $x^{n}+y^{n}…