ABSTRACT
In this chapter we will study https://www.w3.org/1998/Math/MathML"> Σ n 1 https://s3-euw1-ap-pe-df-pch-content-public-p.s3.eu-west-1.amazonaws.com/9780429064630/6df7636a-a9ba-4aa3-a87d-b69f569c8e4c/content/eq_15002.tif" xmlns:xlink="https://www.w3.org/1999/xlink"/> sets of reals. The basic questions we ask are: "Are https://www.w3.org/1998/Math/MathML"> Σ n 1 https://s3-euw1-ap-pe-df-pch-content-public-p.s3.eu-west-1.amazonaws.com/9780429064630/6df7636a-a9ba-4aa3-a87d-b69f569c8e4c/content/eq_15003.tif" xmlns:xlink="https://www.w3.org/1999/xlink"/> sets Lebesgue measurable?" and "Do https://www.w3.org/1998/Math/MathML"> Σ n 1 https://s3-euw1-ap-pe-df-pch-content-public-p.s3.eu-west-1.amazonaws.com/9780429064630/6df7636a-a9ba-4aa3-a87d-b69f569c8e4c/content/eq_15004.tif" xmlns:xlink="https://www.w3.org/1999/xlink"/> sets have the Baire property?" Positive answers to these questions are denoted by https://www.w3.org/1998/Math/MathML"> Σ n 1 ( L ) https://s3-euw1-ap-pe-df-pch-content-public-p.s3.eu-west-1.amazonaws.com/9780429064630/6df7636a-a9ba-4aa3-a87d-b69f569c8e4c/content/eq_15005.tif" xmlns:xlink="https://www.w3.org/1999/xlink"/> and https://www.w3.org/1998/Math/MathML"> Σ n 1 ( B ) https://s3-euw1-ap-pe-df-pch-content-public-p.s3.eu-west-1.amazonaws.com/9780429064630/6df7636a-a9ba-4aa3-a87d-b69f569c8e4c/content/eq_15006.tif" xmlns:xlink="https://www.w3.org/1999/xlink"/> , respectively. In the same spirit, we say that https://www.w3.org/1998/Math/MathML"> Δ n 1 ( L ) https://s3-euw1-ap-pe-df-pch-content-public-p.s3.eu-west-1.amazonaws.com/9780429064630/6df7636a-a9ba-4aa3-a87d-b69f569c8e4c/content/eq_15007.tif" xmlns:xlink="https://www.w3.org/1999/xlink"/> or https://www.w3.org/1998/Math/MathML"> Δ n 1 ( B ) https://s3-euw1-ap-pe-df-pch-content-public-p.s3.eu-west-1.amazonaws.com/9780429064630/6df7636a-a9ba-4aa3-a87d-b69f569c8e4c/content/eq_15008.tif" xmlns:xlink="https://www.w3.org/1999/xlink"/> holds if all https://www.w3.org/1998/Math/MathML"> Δ n 1 https://s3-euw1-ap-pe-df-pch-content-public-p.s3.eu-west-1.amazonaws.com/9780429064630/6df7636a-a9ba-4aa3-a87d-b69f569c8e4c/content/eq_15009.tif" xmlns:xlink="https://www.w3.org/1999/xlink"/> sets are measurable or have the Baire property.
