Hi there, Thanks for your question about running and smoking.
Yes, I do not see why not.
Running has got many benefits for you, physical and mental, regardless of your background.
Things to keep in mind:
Start off easy. A good example of what I mean by easy is my Beginner Running Programs. They follow a run/walk approach and start off with only a few minutes of running. Now, I am not saying you have to follow these programs to the letter. Just use that same approach when you start running.
Under certain "riskier" conditions it might be better if you visit your GP first for a physical check-up. E.g. when you are overweight, over forty, have a history of heart disease in your family, when you have not exercised much before, when you have been a really heavy smoker etc. Your doctor can do a proper check on you and advise what activities you can or cannot do.
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Hope this helps a bit. Well done on making these positive changes in your life. Kind regards, Dominique