MAT337 HOMEWORK 4: DUE MARCH 20
1. (6 points) A subset A of R is said to have the property of Baire if there is an open
subset U of R such that the symmetric difference A4U = (A \ U) ∪ (U \ A) is meager,
i.e., A4U = ⋃∞n=1Xn for some sequence (X)∞n=1 of nowhere dense subsets of R. Prove
that if (An)
∞
n=1 is a sequence of subsets of R with the property of Baire then their union
A =
⋃∞
n=1An also has the property of Baire.
1

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