Graphs of real functions with pathological behaviors

A friend of mine This paper is dedicated to the memory of Franco Montagna. Franco was a dear friend of mine. I guess that, among the people who took part in the Conference in memoriam Franco Montagna, I am the person who has known him for the longest time: we were students together at the university of Pavia in the late Sixties. For our "tesi di laurea", in the early Seventies we went to Ferrara together to speak with Roberto Magari (at that time he was at the University of Ferrara), who was the thesis advisor for both of us. One year later Roberto Magari moved to Siena, and Franco and I obtained a fellowship from the CNR, the Italian science foundation. For many years Franco and I were colleagues and friends in Siena. I wish to recall our first trip to the United States: that time, as well, the two of us went to New York together for a couple of weeks. When I was in Siena, I was invited to have dinner at Franco and Tonina's house many times, I would say uncountably many times (I actually could never count the number of times I went there). In those years Tonina and Franco were true friends for me. Today I would like to say: