1 Product measures Let (X,A , μ) be a σ-finite measure space. Then with A ⊗ A the product σalgebra and μ ⊗ μ the product measure on A ⊗A , (X ×X,A ⊗A , μ⊗ μ) is itself a σ-finite measure space. Write… Expand

Here, instead of taking a σ-algebra as given and then defining a measure on this σ-algebra (namely, on the measurable sets), we take an outer measure as given and then define measurable sets using… Expand

Euler discovered the pentagonal number theorem in 1740 but was not able to prove it until 1750. He sent the proof to Goldbach and published it in a paper that finally appeared in 1760. Moreover,… Expand

If X,Y are normed spaces, let B(X,Y ) be the set of all bounded linear maps X → Y . If T : X → Y is a linear map, I take it as known that T is bounded if and only if it is continuous if and only if E… Expand

In this article, we give a summary of Leonhard Euler’s work on the pentagonal number theorem. First we discuss related work of earlier authors and Euler himself. We then review Euler’s… Expand

What is a wave? Is a wave a “thing”, or is it merely a way of speaking about pieces of stuff changing in a certain way in time? This is related to William of Ockham’s ideas about motion, that… Expand