OOBD

In the same settings you'll find, to which email address the notifications will be send:

But this address is probably not your “normal” address, it is the Google-Mail address which you automatically get when creating your Google account.

So if the address shown like above is not your normal address, you've to make Google Mail to forward all incoming stuff to your normal mail address:

First switch over from your Google Plus screen into the Google Mail section by selecting the Mail menu item:

As next select your Mail settings (again in the upper right corner):

In the settings, you'll find “Forwarding and IMAP/POP”

In there, choose the “Forward” button:

and enter your “normal” email address

.

After pressing “Ok”

you'll get a confirmation mail to your normal email address, containing a link which you need to click to tell Google that your Email address is ok to receive forwarded mails.

After done all that, go again into you Google-Mail-Forward-Settings (if you are still on that page, just press reload in your browser). Finally you should see a picture like that:

Just activate “Copy incoming Mails to…” and save your settings.

Now you will reveive a notification to your normal email address all the time when somebody writes a post in Google Plus, as long as the writer does not forget to turn the “Notification” flag on.