Related papers: On Egorov's Theorem for Infinite Measure
A very short proof of Kneser's theorem via transversal is given.
In this short note a new proof of the monotone con- vergence theorem of Lebesgue integral on \sigma-class is given.
We prove a conjecture of Gromov about non-free isometric immersions.
There are proven few analogues of the Theorem of Moser using The Approximation Theorem of Artin.
We give a very simple proof of a strengthened version of Chernoff's Inequality. We derive the same conclusion from much weaker assumptions.
The main result of this note, Theorem 2, is the following: a Borel measure on the space of infinite Hermitian matrices, that is invariant under the action of the infinite unitary group and that admits well-defined projections onto the…
We survey some basic results on the Gromov-Prohorov distance between metric measure spaces. (We do not claim any new results.) We give several different definitions and show the equivalence of them. We also show that convergence in the…
We give an infinite number of proofs of Pythagoras theorem.Some can be classified as `self-similar proofs'.
We give a short, explicit proof of Hindman's Theorem that in every finite coloring of the integers, there is an infinite set all of whose finite sums have the same color. We give several exampls of colorings of the integers which do not…
In this short paper we show that the inequality of arithmetic and geometric means is reduced to another interesting inequality, and a proof is provided.
We prove in this Note an observation estimate at one point in time for the Kolmogorov equation in the whole space. Such estimate implies the observability and the null controllability for the Kolmogorov equation with a control region which…
We show that for a minimal system $(X,T)$, the set of saturated points along cubes with respect to its maximal $\infty$-step pro-nilfactor $X_\infty$ has a full measure. As an application, it is shown that if a minimal system $(X,T)$ has no…
Generalizing a geometric idea due to J. Sondow, we give a geometric proof for the Cantor's Theorem. Moreover, it is given an irrationality measure for some Cantor series.
The aim of this short note is to present an elementary, self-contained, and direct proof for the classical Lebesgue decomposition theorem.
We prove Shokurov's index conjecture for quotient singularities.
We give a counting based proof of the Graham Pollak Theorem
We give a short proof of Gao's Quantum Union Bound and Gentle Sequential Measurement theorems.
We present simple and direct proof to an important case of Nash-Moser-Ekeland theorem.
We present a relative form of the Toponogov comparison theorem.
We give a simple proof of Bourgain's theorem on the singularity of Ornstein's maps.