Thick sets in Banach spaces

This thesis studies thick sets in Banach spaces, which are defined similarly as the sets of the second Baire category. We show some basic properties of thick and thin sets and their characterizations - mainly the relation with the Uniform Boundedness Principle, the Banach-Steinhaus and Open mapping theorem and w∗ - integrability. Lastly, we give an example of a thick set, which is not of the second Baire category.