Matteo Renzi has tweeted to thank his followers for their support, the new Italian prime minister said: "Thanks for your messages. Tough and difficult task. But we are Italy, we will succeed. A commitment: to remain ourselves, free and simple."
Grazie per i messaggi. Compito tosto e difficile. Ma siamo l'Italia, ce la faremo. Un impegno: rimanere noi stessi, liberi e semplici.
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New 'smart ticketing' plans will also be introduced so travellers can receive automatic compensation payments for late trains.
The 41-year-old father of six died last Thursday - a week before he and the band had been due to begin touring in North America.
There will be heavy showers on Saturday though sunshine will be enjoyed by many across the UK before a similar outlook on Sunday.